#### Title

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

#### Publication Date

2003

#### Journal

Journal of Combinatorial Theory (Series A)

#### Volume

101

#### Issue

1

#### First Page

69

#### Last Page

89

#### Abstract

It is well known that if a finite graded lattice of rank n is supersolvable, then 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 show that a finite graded lattice of rank n is supersolvable if and only if it has such a labeling. We next 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.

#### Recommended Citation

McNamara, Peter. "EL-labelings, Supersolvability and 0-Hecke Algebra Actions on Posets." *Journal of Combinatorial Theory (Series A)* 101, no. 1 (2003)
: 69-89.