In [R.P. Stanley, The descent set and connectivity set of a permutation, J. Integer Seq. 8 (3) (2005) Article 05.3.8] Stanley gives certain enumerative identities revealing a duality between descent sets and connectivity sets of the symmetric group. In this paper we generalize these identities to all Coxeter groups. The proofs are obtained by giving these identities an algebraic explanation in terms of parabolic subgroups, coset representatives, and Poincaré series, and by a formal argument in terms of inclusion-exclusion-like matrices. © 2007 Elsevier Ltd. All rights reserved.
On a duality in Coxeter groups / Marietti, Mario. - In: EUROPEAN JOURNAL OF COMBINATORICS. - ISSN 0195-6698. - STAMPA. - 29:7(2008), pp. 1555-1562. [10.1016/j.ejc.2007.12.001]
On a duality in Coxeter groups
MARIETTI, Mario
2008
Abstract
In [R.P. Stanley, The descent set and connectivity set of a permutation, J. Integer Seq. 8 (3) (2005) Article 05.3.8] Stanley gives certain enumerative identities revealing a duality between descent sets and connectivity sets of the symmetric group. In this paper we generalize these identities to all Coxeter groups. The proofs are obtained by giving these identities an algebraic explanation in terms of parabolic subgroups, coset representatives, and Poincaré series, and by a formal argument in terms of inclusion-exclusion-like matrices. © 2007 Elsevier Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
