Factoring the Poincaré polynomials for the Bruhat order on \(S_n\)

DOI10.1006/jcta.1997.2861zbMath0935.05087OpenAlexW2013350506MaRDI QIDQ1268614

Vesselin N. Gasharov

Publication date: 4 May 2000

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcta.1997.2861

zbMATH Keywords

Poincaré polynomialBruhat order

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Grassmannians, Schubert varieties, flag manifolds (14M15)

Related Items (13)

Billey-Postnikov decompositions and the fibre bundle structure of Schubert varieties ⋮ Rationally smooth Schubert varieties and inversion hyperplane arrangements ⋮ Pattern characterization of rationally smooth affine Schubert varieties of type \(A\) ⋮ On automorphisms of undirected Bruhat graphs ⋮ Self-dual intervals in the Bruhat order ⋮ Rationally smooth elements of Coxeter groups and triangle group avoidance. ⋮ Enumeration by associated reflections on Coxeter systems ⋮ Bruhat order, smooth Schubert varieties, and hyperplane arrangements ⋮ Betti numbers of smooth Schubert varieties and the remarkable formula of Kostant, Macdonald, Shapiro, and Steinberg ⋮ Enumerating \(S_n\) by associated transpositions and linear extensions of finite posets ⋮ Pattern avoidance and rational smoothness of Schubert varieties ⋮ The parabolic map ⋮ Poincaré Polynomials of Odd Diagram Classes

Cites Work

• Unnamed Item
• Unnamed Item
• Criterion for smoothness of Schubert varieties in Sl(n)/B
• Classical Bruhat orders and lexicographic shellability
• Pattern avoidance and rational smoothness of Schubert varieties
• A generalization of the Kostant—Macdonald identity
• Local poincaré duality and non-singularity of schubert varieties

This page was built for publication: Factoring the Poincaré polynomials for the Bruhat order on \(S_n\)