Shortest path poset of Bruhat intervals

被引：0

作者：

Saúl A. Blanco

机构：

[1] DePaul University,Department of Mathematical Sciences

来源：

Journal of Algebraic Combinatorics | 2013年 / 38卷

关键词：

Shortest paths; Bruhat graph; Bruhat order; -polynomials; Complete ; -index;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We define the shortest path poset SP(u,v) of a Bruhat interval [u,v], by considering the shortest u–v paths in the Bruhat graph of a Coxeter group W, where u,v∈W. We consider the case of SP(u,v) having a unique rising chain under a reflection order and show that in this case SP(u,v) is a Gorenstein∗ poset. This allows us to derive the nonnegativity of certain coefficients of the complete cd-index. We furthermore show that the shortest path poset of an irreducible, finite Coxeter group exhibits a symmetric chain decomposition.

引用

页码：585 / 596

页数：11

共 14 条

[1]

Billera L.J.(2011)Quasisymmetric functions and Kazhdan–Lusztig polynomials Isr. J. Math. 184 317-348

[2]

Brenti F.(1998)Pattern avoidance and rational smoothness of Schubert varieties Adv. Math. 139 141-156

[3]

Billey S.C.(2011)The complete Electron. J. Comb. 18 448-472

[4]

Blanco S.A.(1997)-index of dihedral and universal Coxeter groups J. Lond. Math. Soc. (2) 55 91-115

[5]

Brenti F.(1993)Combinatorial expansions of Kazhdan–Lusztig polynomials Compos. Math. 89 2591-2595

[6]

Dyer M.J.(2001)Hecke algebras and shellings of Bruhat intervals Proc. Am. Math. Soc. 129 225-251

[7]

Dyer M.J.(2007)On minimal lengths of expressions of Coxeter group elements as products of reflections J. Algebr. Comb. 26 80-88

[8]

Ehrenborg R.(1976)Decomposition theorem for the J. Comb. Theory, Ser. A 20 701-718

[9]

Karu K.(2006)-index of Gorenstein posets Compos. Math. 142 193-206

[10]

Greene C.(1991)Strong versions of Sperner’s theorem Discrete Math. 98 undefined-undefined

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