Saúl A. Blanco - Shortest path poset of finite Coxeter groups

dmtcs:2721 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2721
Shortest path poset of finite Coxeter groupsConference paper

Authors: Saúl A. Blanco 1

  • 1 Department of Mathematics [Cornell]

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,w0. We show that this poset is the union of Boolean posets of rank absolute length of w0; that is, any shortest path labeled by reflections t1,,tm is fully commutative. This allows us to give a combinatorial interpretation to the lowest-degree terms in the complete cd-index of W.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: Coxeter group,Bruhat order,Boolean poset,complete cd-index.,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Quasisymmetric Functions and Eulerian Enumeration; Funder: National Science Foundation; Code: 0555268

1 Document citing this article

Consultation statistics

This page has been seen 263 times.
This article's PDF has been downloaded 252 times.