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Showing 1 to 6 of 6 for “"Schubert polynomials"”.
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B and D analogues of stable Schubert polynomials and related insertion algorithms
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995.
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Prism tableaux and alternating sign matrices
A. Lascoux and M.-P. Schutzenberger introduced Schubert polynomials to study the cohomology ring of the complete flag variety Fl(C^n). Each Schubert polynomial corresponds to the class defined by a Schubert variety X_w in Fl(C^n). Schubert polynomials are indexed by elements of the symmetric group …
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Matrix Schubert varieties for the affine Grassmannian
Schubert calculus has become an indispensable tool for enumerative geometry. It concerns the multiplication of Schubert classes in the cohomology of flag varieties, and is typically conducted using algebraic combinatorics by way of a polynomial ring presentation of the cohomology ring. The …
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New combinatorics of the weak and strong Bruhat orders
… and strong Bruhat orders, specializations of Schubert polynomials, separable elements in finite Weyl groups, and inequalities for linear extensions of finite posets.
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Root polytopes, triangulations, and subdivision algebras
… the main outstanding problem of modern Schubert calculus, that of finding a combinatorial interpretation for the structure constants of Schubert polynomials. Using a geometric understanding of the relations of Kirillov's algebras in terms of subdivisions of root polytopes, several …
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Polynomials in algebraic combinatorics
… functions, quasisymmetric functions, and polynomials. Classically, these bases are homogeneous functions, however, the introduction of K-theoretic combinatorics has led to increased interest in finding inhomogeneous deformations of classical bases. Joint with A. Yong and N. Tokcan, we …