Extremal matrices for the Bruhat-graph order
نویسندگان
چکیده
منابع مشابه
A Monoid for the Grassmannian Bruhat Order
Structure constants for the multiplication of Schubert polynomials by Schur symmetric polynomials are related to the enumeration of chains in a new partial order on S 1 , the Grassmaniann Bruhat order. Here we present a monoid M related to this order. We develop a notion of reduced sequences for M and show that M is analogous to the nil-Coxeter monoid for the weak order on S 1 .
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 کاملAn Improved Tableau Criterion for Bruhat Order
To decide whether two permutations are comparable in Bruhat order of Sn with the well-known tableau criterion requires ( n 2 ) comparisons of entries in certain sorted arrays. We show that to decide whether x ≤ y only d1 + d2 + . . .+ dk of these comparisons are needed, where {d1, d2, . . . , dk} = {i|x(i) > x(i+1)}. This is obtained as a consequence of a sharper version of Deodhar’s criterion,...
متن کاملPattern avoidance and the Bruhat order
The structure of order ideals in the Bruhat order for the symmetric group is elucidated via permutation patterns. A method for determining nonisomorphic principal order ideals is described and applied for small lengths. The permutations with boolean principal order ideals are characterized. These form an order ideal which is a simplicial poset, and its rank generating function is computed. More...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear and Multilinear Algebra
سال: 2020
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081087.2020.1749540