Two generalizations of posets of shuffles

Authors:
Patricia Hersh
Affiliations:
Department of Mathematics, University of Washington, Box 354350, Seattle, Washington
Venue:
Journal of Combinatorial Theory Series A
Year:
2002

Citing 4
Cited 1

Enumerative combinatorics

Enumerative combinatorics
Posets of shuffles

Journal of Combinatorial Theory Series A
Shuffling lattices

Journal of Combinatorial Theory Series A
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

Chain decomposition and the flag f-vector

Journal of Combinatorial Theory Series A

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Abstract

We study posets defined by Stanley as a multiset generalization of Greene's posets of shuffles. Ehrenborg defined a quasi-symmetric function encoding for the flag f-vector, denoted FP, and we determine FP for shuffle posets of multisets, expressing it as a Schur-positive symmetric function. This leads to several combinatorial formulas as well as proofs that shuffle posets of multisets are super-solvable and have symmetric chain decompositions. We also generalize posets of shuffles to posets for shuffling k words, answering a question of Stanley. Finally, we extend our results about shuffle posets of multisets to k-shuffle posets.