EL-labelings, Supersolvability and 0-Hecke Algebra Actions on Posets

2001/11/30 by Peter McNamara · 1 citation
Mathematics · #math.CO #msc:06A11 #msc:05E99

paper · pdf

published as Journal of Combinatorial Theory (Series A) 101 (2003), 69-89 · 18 pages, 8 figures. Added JCTA reference and included some minor corrections suggested by referee

arxiv created 2003/03/10 · arxiv updated 2009/11/30

Abstract

We show that a finite graded lattice of rank n is supersolvable if and only if it has an EL-labeling where the labels along any maximal chain form a permutation. We call such a labeling an S_n EL-labeling and we consider finite graded posets of rank n with unique top and bottom elements that have an S_n EL-labeling. We describe a type A 0-Hecke algebra action on the maximal chains of such posets. This action is local and gives a representation of these Hecke algebras whose character has characteristic that is closely related to Ehrenborg's flag quasi-symmetric function. We ask what other classes of posets have such an action and in particular we show that finite graded lattices of rank n have such an action if and only if they have an S_n EL-labeling.

Cited by

• Convex Geometries via Hopf Monoids: Combinatorial Invariants, Reciprocity, and Supersolvability

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• The Whitney Duals of a Graded Poset
• Exceptional sequences in semidistributive lattices and the poset topology of wide subcategories
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