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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. horizontal gradient; horizontal curve; horizontal critical point; standard Engel structure; limit of trajectories; transversality; semi-algebraic set | 0 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. \(\lambda \) -rings; Chern classes; Adams operations; Riemann-Roch theorem; K-group; local complete intersection morphism of schemes W. Fulton and S. Lang, \textit{Riemann-Roch Algebra}, Grundlehren der Mathematischen Wissenschaften, Vol. 277, Springer-Verlag, New York, 1985. | 0 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. complete intersection; derived category; hypersurface; noetherian scheme; prime thick subcategory; singularity category; spectrum; triangulated category | 0 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. real analytic curves; isolated critical points; the number of branches; half-branches; topological degree; non-complete intersection; double points; triple points | 0 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. equisingular deformation; hypersurfaces; geometric genus; codimension; intersection theory; singularities of hyperplane sections G. Xu, Divisors on hypersurfaces, Math. Zeitschrift 219 (1995), 581--589. | 0 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. liaison of curves; Buchsbaum ring; ideal intersection; local cohomology P. Schenzel and W. Vogel, On liaison and arithmetical Buchsbaum curves inP3, preprint. | 0 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Calabi-Yau threefold; threefold of general type; Chern ratios; number of nodes; complete intersection Chang M.C., Lopez A.F. (2001). A linear bound on the Euler number of threefolds of Calabi--Yau and of general type. Manuscripta Math. 105:47--67 | 0 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. quasi-complete intersection; almost complete intersections Stückrad, J. (1992). On quasi-complete intersections. Archiv der Mathematik 58, 529--538. | 1 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Buchsbaum-Eisenbud criterion; prime ideal of the monomial curve; minimal finite free resolution H. Bresinsky, Minimal free resolutions of monomial curves in \(\mathbb{P}\) k 3 . Linear Alg. Appl.59, 121--129 (1984) | 0 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. equations defining a subscheme; polynomial algebra; minimal system of homogeneous generators Dario Portelli and Walter Spangher, On the equations which are needed to define a closed subscheme of the projective space, J. Pure Appl. Algebra 98 (1995), no. 1, 83 -- 93. | 0 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. algebraic geometry Severi, Über die Darstellung algebraischer Mannigfaltigkeiten als Durchschnitte von Formen, Abh. math. Sem. Hansische Univ. 15 pp 97-- (1943) | 0 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. generated sets of projected Veronesean ideals Bresinsky, H.; Renschuch, B.: Basisbestimmung veronesescher projektionsideale mit allgemeiner nullstelle (tm0, tm-r0tr1, tm-s0ts1, tm1). Math. nachr. 96, 257-269 (1980) | 0 |
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Projective geometry, algebraic geometry Perron, Über das Vahlensche Beispiel zu einem Satz von Kronecker, Math. Ann., Berlin 118 pp 441-- (1942) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double Schubert polynomials; equivariant cohomology Ikeda, T.; Mihalcea, L.; Naruse, H., \textit{double Schubert polynomials for the classical groups}, Adv. Math., 226, 840-886, (2011) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schur functions; Schubert polynomials; conjecture of Fomin and Kirillov; Grothendieck polynomial Lenart, C., Noncommutative Schubert calculus and Grothendieck polynomials.Adv. Math., 143 (1999), 159--183. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert classes; symplectic Grassmannians; torus equivariant cohomology; Giambelli type formula; Wilson's conjecture; double Schubert polynomials Ikeda, T.; Matsumura, T., \textit{Pfaffian sum formula for the symplectic Grassmannians}, Math. Z., 280, 269-306, (2015) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double Schubert polynomials Buch, Anders S.; Rimányi, Richárd, Specializations of Grothendieck polynomials, C. R. Math. Acad. Sci. Paris, 339, 1, 1-4, (2004) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Dunkl and Gaudin operators at critical level; Catalan numbers, Schroder numbers; Schubert polynomials; Grothendieck polynomials A. N. Kirillov, \textit{On Some Combinatorial and Algebraic Properties of Dunkl Elements}, RIMS preprint, 2012. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Dunkl operators at critical level; Gaudin operators at critical level; Catalan numbers; Schröder numbers; Schubert polynomials; Grothendieck polynomials | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double Schubert polynomials; degeneracy loci; map of flagged vector bundles; Chow ring; Chern roots; determinantal formula W. Fulton, ``Flags, Schubert polynomials, degeneracy loci, and determinantal formulas'', Duke Math. J. 65 (1992), 381--420. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials universal Schubert polynomials; quantum Schubert polynomials; partial flag varieties; double Schubert polynomials; degeneracy loci; Chern classes Fulton W. (1999). Universal Schubert polynomials. Duke Math. J. 96(3): 575--594 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Littlewood-Richardson rule; double symmetric functions; equivariant Schubert classes; Grassmannians; quantum immanants; Schur functions; Littlewood-Richardson polynomials; combinatorics of puzzles; Casimir elements; general linear Lie algebra Alexander I. Molev, ``Littlewood-Richardson polynomials'', J. Algebra321 (2009) no. 11, p. 3450-3468 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert varieties; quantum double Schubert polynomials; Schur functions; Schubert polynomials; morphisms of vector bundles; degeneracy loci; Grassmannians; flag manifolds; symmetric functions Fulton, W., Pragacz, P.: Schubert Varieties and Degeneracy Loci. Lecture Notes in Mathematics, vol. 1689. Springer, Berlin (1998) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Grothendieck polynomials; Coxeter systems; reduced words | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert varieties; Gröbner bases; Grothendieck polynomials; simplicial complexes | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials factorial Grothendieck polynomials; flagged partitions; flagged set-valued tableaux; vexillary permutations; Jacobi-Trudi formula; double Grothendieck polynomials | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Yang-Baxter equations; Hecke algebra; flag varieties; Schubert polynomials; Grothendieck polynomials Lascoux, A.; Leclerc, B.; Thibon, J. -Y: Flag varieties and the Yang--Baxter equation. Lett. math. Phys. 40, No. 1, 75-90 (1997) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck polynomials; Schur polynomials; Pieri formula; Schubert polynomials; Schubert classes; Grassmannian permutations Lenart, C., Combinatorial aspects of the \(K\)-theory of Grassmannians, Ann. Comb., 4, 1, 67-82, (2000) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double Grothendieck polynomials; key polynomials; 0-Hecke algebra; sorting operators; Bruhat order; Pieri formula Pons, V.: Interval structure of the Pieri formula for Grothendieck polynomials, Internat. J. Algebra comput. 23, 123-146 (2013) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials flag varieties; Schubert polynomials; Grothendieck polynomials; simplicial complexes | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double Schubert polynomials; flagged Schur polynomials, reverse double Schubert polynomials | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials quantum double Schubert polynomials; Ehresmann-Bruhat graph; quantum Pieri's rule; cohomology; flag manifold Kirillov, A. N.; Maeno, T.: Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-intriligator formula. Discrete math. 217, No. 1-3, 191-223 (2000) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials combinatorial Hopf algebras; noncommutative symmetric functions; quasisymmetric functions; Malvenuto-Reutenauer Hopf algebras; dualities; coproducts; Grothendieck polynomials; K-theory; Schubert varieties; generating series; set-valued tableaux; Schur functions; bialgebras Lam, Thomas; Pylyavskyy, Pavlo, Combinatorial Hopf algebras and \(K\)-homology of grassmanians, Int. Math. Res. Not., 2007, 24, (2007) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Eta polynomials; double eta polynomials; Giambelli polynomials; Young raising operators; Schubert calculus; equivariant cohomology Tamvakis, H., \textit{double eta polynomials and equivariant Giambelli formulas}, J. Lond. Math. Soc. (2), 94, 209-229, (2016) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck polynomials; projective degree of Schubert cycles; flag manifolds; symmetrizing operators; Ehresmanoeder; Schubert polynomials; Pieri formula; enumerative geometry; Root systems; Coxeter groups; Young tableaux; cohomology ring; Grothendieck ring Lascoux, Alain and Schützenberger, Marcel-Paul, Symmetry and flag manifolds, Invariant Theory ({M}ontecatini, 1982), Lecture Notes in Math., 996, 118-144, (1983), Springer, Berlin | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials vexillary permutations; Lascoux-Schützenberger's double Grothendieck polynomials; degeneracy loci | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials flag manifold; equivariant cohomology; double Schubert polynomials; Pieri formula; equivariant Schubert structure constants Shawn Robinson, A Pieri-type formula for \?*_{\?}(\?\?_{\?}(\Bbb C)/\?), J. Algebra 249 (2002), no. 1, 38 -- 58. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials group algebra; permutations; symmetrizing operators; Newton's divided differences; Grothendieck polynomials; Schubert polynomial Lascoux, Alain; Schützenberger, Marcel-Paul, Décompositions dans l'algèbre des différences divisées, Discrete Math., 99, 1-3, 165-179, (1992) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials flag manifold; Schubert varieties; Bruhat order; saturated chains; harmonic polynomials; Grothendieck ring; Demazure modules; Schubert polynomials; flagged Schur polynomials; 312-avoiding permutations; Kempf elements; vexillary permutations; Gelfand-Tsetlin polytope; toric degeneration; parking functions; binary trees Postnikov, A.; Stanley, R., Chains in the Bruhat order, J. Algebr. Comb., 46, 133-174, (2009) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert calculus; spherical orbits; Grothendieck polynomials; \(K\)-theory; degeneracy loci | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck ring; structure sheaves of Schubert varieties; Grothendieck polynomials; cohomology ring of the flag variety Lascoux, A., Anneau de Grothendieck de la variété de drapeaux, (The Grothendieck Festschrift, Vol. III, Progr. Math., vol. 88, (1990), Birkhäuser Boston Boston, MA), 1-34 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials symmetric polynomials; Grothendieck polynomials; \(K\)-theory; Grassmannians; Schubert varieties | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials weighted flag varieties; equivariant cohomology; Schubert classes; double Schubert polynomials | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Grothendieck polynomials Lascoux, A., Schubert & Grothendieck: un bilan bidécennal, Sém. Lothar. Combin., 50, (2003/04) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double Schubert polynomials; excited Young diagrams; Schur P-functions; Schur Q-functions; divided difference operators; torus equivarant cohomology T. Ikeda, H. Naruse, Double Schubert polynomials of classical type and Excited Young diagrams, Kôkyûroku Bessatsu B11 (2009). | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Sage-Combinat distribution; Schubert polynomials; key polynomials; Grothendieck polynomials; non-symmetric Macdonald polynomials | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert varieties; Gröbner bases; Grothendieck polynomials; simplicial complexes | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Grothendieck polynomials; Coxeter systems; reduced words | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Bruhat order; Schur functions; permutations; divided differences; Schubert polynomials Macdonald, I. G., Notes on Schubert polynomials, (1991), Publications du Laboratoire de Combinatoire et D'informatique Mathématique, Dép. de Mathématiques et D'informatique, Universitédu Québec à Montréal, available at | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schur function; Schubert polynomials; Schur polynomials; Schubert functions; Baxter operator; reduced words of permutations Winkel, R.: Schubert functions and the number of reduced words of permutations, Sém. lothar. Combin. 39, 1-28 (1997) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Kazhdan-Lusztig conjecture; symmetrizable Kac-Moody Lie algebras; \({\mathcal D}\)-modules; flag variety; representations; geometry of Schubert varieties; Kazhdan-Lusztig polynomials; mixed Hodge modules O.J. Ganor, \textit{Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings}, \textit{Phys. Rev.}\textbf{D 97} (2018) 041901 [arXiv:1710.06880] [INSPIRE]. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Kraśkiewicz-Pragacz modules; highest weight categories; ringel duality; B-modules | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials plane partitions; MacMahon's formulas; dual Grothendieck polynomials; volume generating functions | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials stable (canonical) Grothendieck polynomials; hook-valued tableaux; crystal bases; uncrowding algorithm | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials box diagrams; diagram rules; tableaux; Schubert polynomials; symmetric functions; Schur functions R. Winkel. ''Diagram rules for the generation of Schubert polynomials''. J. Combin. Theory Ser. A 86 (1999), pp. 14--48.DOI. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double affine Hecke algebras; Askey-Wilson polynomials; Poisson cohomology; Hochschild cohomology; universal deformations Oblomkov, A., \textit{double affine Hecke algebras of rank 1 and affine cubic surfaces}, Int. Math. Res. Not. IMRN, 2004, 877-912 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Deligne-Lusztig varieties; \(K\)-theory; Grothendieck polynomials; degeneracy loci | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; symmetric functions; Monk's formula; divided differences Kohnert, A.; Veigneau, S.: Using Schubert basis to compute with multivariate polynomials. Adv. appl. Math. 19, 45-60 (1997) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Bruhat orderings; Kazhdan-Lusztig polynomials; Schubert varieties; Coxeter groups F. du Cloux, ''Rigidity of Schubert closures and invariance of Kazhdan-Lusztig polynomials,'' Adv. in Math. 180 (2003), 146--175. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Weyl groups; Coxeter groups; representations of Hecke algebras; Jordan-Hölder series of Verma modules; irreducible highest weight modules; Weyl character formula; primitive ideals in enveloping algebras; complex semisimple Lie algebras; local Poincaré duality; geometry of Schubert cells; flag varieties; intersection cohomology; Laurent polynomials; intertwining operators; finite Chevalley groups; affine Weyl groups; cohomology groups; simple reflections; highest weight representations; Cartan subalgebras D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, \textit{Invent.} \textit{Math.}, 53 (1979), no. 2, 165--184.Zbl 0499.20035 MR 560412 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Demazure characters; key polynomials; fundamental slide polynomials | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schur functions; \(\lambda\)-rings; Cauchy kernel; Euclidean algorithm; continued fractions; Padé approximation; divided differences; cohomology of Grassmannian; orthogonal polynomials; Schubert polynomials Lascoux, A.: Symmetric functions \& combinatorial operators on polynomials. CBMS reg. Conf. ser. Math. 99 (2003) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials coinvariant algebra; Kazhdan-Lusztig cells; Schubert polynomials; character formula; irreducible representations; symmetric group Y. Roichman, Schubert polynomials, Kazhdan--Lusztig basis and characters, (with an, appendix: On characters of Weyl groups, co-authored with, R. M. Adin, and, A. Postnikov, ), Discrete Math, to appear. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials symmetric Grothendieck polynomials; Newton polytopes | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck polynomials; \(K\)-theory; 0-Hecke monoid; insertion algorithm; factor sequence formula Buch, A.; Kresch, A.; Shimozono, M.; Tamvakis, H.; Yong, A., Stable Grothendieck polynomials and \textit{K}-theoretic factor sequences, Math. Ann., 340, 359-382, (2008) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials symmetric polynomials; Grothendieck polynomials; \(K\)-theory; set-valued tableaux; 321-avoiding permutations | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials representation theory; reductive algebraic groups; simple modules; highest weights; character formulas; Weyl's character formula; affine group schemes; injective modules; injective resolutions; derived functors; Hochschild cohomology groups; hyperalgebra; split reductive group schemes; Steinberg's tensor product theorem; irreducible representations; Kempf's vanishing theorem; Borel-Bott-Weil theorem; characters; linkage principle; dominant weights; filtrations; Steinberg modules; cohomology rings; rings of regular functions; Schubert schemes; line bundles; Schur algebras; quantum groups; Kazhdan-Lusztig polynomials J. C. Jantzen, \textit{Representations of Algebraic Groups. Second edition}, Amer. Math. Soc., Providence (2003). | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Stanley symmetric functions; Schubert polynomials; Littlewood-Richardson rule | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Kazhdan-Lusztig polynomials; Schubert varieties; small resolutions | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; permutation patterns | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials quiver polynomials; Grothendieck polynomials; iterated residues; equivariant K theory Allman, Justin, Grothendieck classes of quiver cycles as iterated residues, Michigan Math. J., 63, 4, 865-888, (2014) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Castelnuovo-Mumford regularity; ladder determinantal ideal; matrix Schubert variety; Grassmannian; Grothendieck polynomial | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Kazhdan-Lusztig polynomials; Schubert varieties; intersection cohomology P. Polo, Construction of arbitrary Kazhdan-Lusztig polynomials in symmetric groups, \textit{Repre-} \textit{sent. Theory}, 3 (1999), 90--104.Zbl 0968.14029 MR 1698201 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Schubert functors; Kraśkiewicz-Pragacz modules; Schubert calculus | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials quantum cohomology; Grassmannians; positivity; Gromov-Witten invariant; Schubert basis; quantum Schubert polynomials; flag varieties; symmetric functions; Seidel representation | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Kazhdan-Lusztig polynomials; Schubert varieties; intersection cohomology | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials diagram; tableaux; Subert polynomials; symmetric functions; Schubert module S. Fomin, C. Greene, V. Reiner, and M. Shimozono, ''Balanced labellings and Schubert polynomials,'' European J. Combin. 18 (1997), no. 4, 373--389. the electronic journal of combinatorics 25(3) (2018), #P3.4622 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Demazure operator formula | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Smith's theorem; Laurent polynomials; Grothendieck's theorem; vector bundles | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials symmetric polynomials; divided differences; intersection theory; symmetric functions; polynomials universally supported on degeneracy loci; flag degeneracy loci; flag varieties; Grassmannians; Schubert varieties; Schur polynomials; \(Q\)-polynomials; determinants; Pfaffians; Weyl groups; Young-Ferrers' diagrams; Segre classes; tensor bundles; Gysin maps; vector bundles; Schur bundles; vanishing theorem P. Pragacz, ''Symmetric polynomials and divided differences in formulas of intersection theory,'' in Parameter Spaces, Warsaw: Polish Acad. Sci., 1996, vol. 36, pp. 125-177. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; factorial and \(q\)-factorial Schur functions; factorization Prosper, V.: Factorization properties of the q-specialization of Schubert polynomials, Ann. comb. 4, 91-107 (2000) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Baxter operator; Lehmer code; Schubert polynomials; Schur functions; Young tableaux; Macdonald polynomials; weak Brunat order on Coxeter groups; Poincaré polynomials; reduced words | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Lagrange singularities; Thom polynomials; \(\widetilde{Q}\)-functions; jets; numerical positivity; Schubert calculus; isotropic Grassmanians M. Mikosz, P. Pragacz and A. Weber, Positivity of Thom polynomials II: the Lagrange singularities, Fund. Math. 202 (2009), 65-79. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Demazure characters | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Schubert complexes; degeneracy loci; balanced labelings; Thom-Porteous formula | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials representation of the symmetric group; Pieri rule; Gromov-Witten invariants; Schubert polynomials; cohomology ring of the flag manifold; divided difference operators; quadratic associative algebra; Dunkl operators; Schubert calculus; quantum cohomology Fomin, Sergey; Kirillov, Anatol N., Quadratic algebras, Dunkl elements, and Schubert calculus. Advances in geometry, Progr. Math. 172, 147-182, (1999), Birkhäuser Boston, Boston, MA | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Young tableaux; Ferrers shape; reduced words; identity; Stanley's formula; Macdonald's formula; Schubert polynomials; enumeration of plane partitions; permutations; shapes; \(q\)-analogues S. Fomin and A. N. Kirillov, \textit{Reduced words and plane partitions}, J. Algebraic Combin., 6 (1997), pp. 311--319. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Kraśkiewicz-Pragacz modules | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double affine Hecke algebras; nil-DAHAs; nonsymmetric Macdonald polynomials; Whittaker functions; core subalgebras; induced representations I. Cherednik and D. Orr. ''One-dimensional nil-DAHA and Whittaker functions II''. Trans form. Groups 18 (2013), pp. 23--59.DOI. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schur functions; Schubert polynomials; Schubert classes; cohomology ring; flag variety; Lie group; orthogonal groups; symplectic groups; divided difference equations; Billey-Jockusch-Stanley formula; Stanley symmetric functions; Schubert varieties Billey, S.; Haiman, M., \textit{Schubert polynomials for the classical groups}, J. Amer. Math. Soc., 8, 443-482, (1995) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials tableaux; Grothendieck polynomials; \(k\)-Schur functions; affine Grassmannian J. Morse. ''Combinatorics of the K-theory of affine Grassmannians''. Adv. Math. 229 (2012), pp. 2950--2984.DOI. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials dual stable Grothendieck polynomials; reverse plane partitions; crystal operators; Littlewood-Richardson rule Galashin, P., A Littlewood-Richardson rule for dual stable Grothendieck polynomials | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Kraśkiewicz-Pragacz modules Watanabe, M.: An approach toward Schubert positivities of polynomials using kraśkiewicz-pragacz modules. European J. Combin. 58, 17-33 (2016) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; rc-graphs; Monk's rule; Pieri's rule N. Bergeron and S. Billey. ''RC-graphs and Schubert polynomials''. Experiment. Math. 2 (1993), pp. 257--269.DOI. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials R. Winkel. ''A derivation of Kohnert's algorithm from Monk's rule''. Sém. Lothar. Combin. 48 (2002), Art. B48f.URL. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Lagrangian flag manifolds; Lagrangian degeneracy loci; Schubert polynomials; Giambelli-type formula Lascoux, A; Pragacz, P, Operator calculus for \({\widetilde{Q}}\)-polynomials and Schubert polynomials, Adv. Math., 140, 1-43, (1998) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck polynomials; bumpless pipe dreams; alternating sign matrices | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert polynomials; Pieri rule; symmetric polynomial Assaf, S., Bergeron, N., Sottile, F.: On the multiplication of Schubert polynomials. In preparation | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials generalized Demazure atoms; key polynomials; Schubert positivity; nonsymmetric Macdonald polynomials; skyline filings | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials noncommutative version of Schubert polynomials; functoriality A. Lascoux and M.-P. Schützenberger, Fonctorialité des polynômes de Schubert, Invariant theory (Denton, TX, 1986) Contemp. Math., vol. 88, Amer. Math. Soc., Providence, RI, 1989, pp. 585 -- 598 (French, with English summary). | 0 |
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