Weighted enumeration of Bruhat chains in the symmetric group
نویسندگان
چکیده
منابع مشابه
A Weighted Enumeration of Maximal Chains in the Bruhat Order
Given a finite Weyl group W with root system , assign the weight α ∈ to each covering pair in the Bruhat order related by the reflection corresponding to α. Extending this multiplicatively to chains, we prove that the sum of the weights of all maximal chains in the Bruhat order has an explicit product formula, and prove a similar result for a weighted sum over maximal chains in the Bruhat order...
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In this paper we study the partially ordered set of the involutions of the symmetric group Sn with the order induced by the Bruhat order of Sn . We prove that this is a graded poset, with rank function given by the average of the number of inversions and the number of excedances, and that it is lexicographically shellable, hence Cohen-Macaulay, and Eulerian.
متن کاملChains in the Bruhat Order
We study a family of polynomials whose values express degrees of Schubert varieties in the generalized complex flag manifold G/B. The polynomials are given by weighted sums over saturated chains in the Bruhat order. We derive several explicit formulas for these polynomials, and investigate their relations with Schubert polynomials, harmonic polynomials, Demazure characters, and generalized Litt...
متن کاملChains in the Bruhat order
We study a family of polynomials whose values express degrees of Schubert varieties in the generalized complex flag manifold G/B. The polynomials are given by weighted sums over saturated chains in the Bruhat order. We derive several explicit formulas for these polynomials, and investigate their relations with Schubert polynomials, harmonic polynomials, Demazure characters, and generalized Litt...
متن کاملThe Bruhat order on conjugation-invariant sets of involutions in the symmetric group
Let In be the set of involutions in the symmetric group Sn, and for A ⊆ {0, 1, . . . , n}, let F n = {σ ∈ In | σ has a fixed points for some a ∈ A}. We give a complete characterisation of the sets A for which F n , with the order induced by the Bruhat order on Sn, is a graded poset. In particular, we prove that F {1} n (i.e., the set of involutions with exactly one fixed point) is graded, which...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2020
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/15005