# Shortest path poset of finite Coxeter groups

Abstract : We define a poset using the shortest paths in the Bruhat graph of a finite Coxeter group $W$ from the identity to the longest word in $W, w_0$. We show that this poset is the union of Boolean posets of rank absolute length of $w_0$; that is, any shortest path labeled by reflections $t_1,\ldots,t_m$ is fully commutative. This allows us to give a combinatorial interpretation to the lowest-degree terms in the complete $\textbf{cd}$-index of $W$.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [7 references]

https://hal.inria.fr/hal-01185413
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 20, 2015 - 11:08:29 AM
Last modification on : Thursday, July 4, 2019 - 11:38:01 AM
Long-term archiving on: : Wednesday, April 26, 2017 - 9:46:54 AM

### File

dmAK0116.pdf
Publisher files allowed on an open archive

### Identifiers

• HAL Id : hal-01185413, version 1

### Citation

Saúl A. Blanco. Shortest path poset of finite Coxeter groups. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.189-200. ⟨hal-01185413⟩

Record views