Enumerative combinatorics
Journal of Algebraic Combinatorics: An International Journal
Flag-symmetry of the poset of shuffles and a local action of the symmetric group
Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
Discrete Mathematics
Journal of Combinatorial Theory Series A
Poset edge-labellings and left modularity
European Journal of Combinatorics
The sorting order on a Coxeter group
Journal of Combinatorial Theory Series A
Journal of Algebraic Combinatorics: An International Journal
A lexicographic shellability characterization of geometric lattices
Journal of Combinatorial Theory Series A
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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 Sn 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 0' and 1' that have an Sn 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 quasisymmetric 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 Sn EL-labeling.