Mathematics – Combinatorics
Scientific paper
2001-11-13
Journal of Combinatorial Theory (Series A) 101 (2003), 69-89
Mathematics
Combinatorics
18 pages, 8 figures. Added JCTA reference and included some minor corrections suggested by referee
Scientific paper
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.
No associations
LandOfFree
EL-labelings, Supersolvability and 0-Hecke Algebra Actions on Posets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with EL-labelings, Supersolvability and 0-Hecke Algebra Actions on Posets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and EL-labelings, Supersolvability and 0-Hecke Algebra Actions on Posets will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-632204