Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley

DOI10.5802/alco.93zbMath1436.05125arXiv1812.00321OpenAlexW3014632554WikidataQ123189858 ScholiaQ123189858MaRDI QIDQ1985353

Zachary Hamaker, Oliver Pechenik, Anna E. Weigandt, David E. Speyer

Publication date: 7 April 2020

Published in: Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.00321

zbMATH Keywords

Schubert polynomialweak orderSperner propertyMacdonald identity

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Determinants, permanents, traces, other special matrix functions (15A15) Combinatorics of partially ordered sets (06A07) Grassmannians, Schubert varieties, flag manifolds (14M15) Group actions on combinatorial structures (05E18)

Related Items (10)

Regularity of matrix Schubert varieties ⋮ On \(\mathfrak{sl}(N)\) link homology with \(\bmod N\) coefficients ⋮ Asymmetric Function Theory ⋮ Weighted enumeration of Bruhat chains in the symmetric group ⋮ A combinatorial 𝔰𝔩₂-action and the Sperner property for the weak order ⋮ Gröbner geometry of Schubert polynomials through ice ⋮ A combinatorial duality between the weak and strong Bruhat orders ⋮ The weak Bruhat order on the symmetric group is Sperner ⋮ Tableau posets and the fake degrees of coinvariant algebras ⋮ The Sperner property for 132‐avoiding intervals in the weak order

Cites Work

• Unnamed Item
• Schubert polynomials and the nilCoxeter algebra
• A bijective proof of Macdonald's reduced word formula
• Product evaluations of Lefschetz determinants for Grassmannians and of determinants of multinomial coefficients
• A combinatorial duality between the weak and strong Bruhat orders
• The weak Bruhat order on the symmetric group is Sperner
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• RC-Graphs and Schubert Polynomials

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