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Two Generalizations of Posets of Shuffles

โœ Scribed by Patricia Hersh

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
308 KB
Volume
97
Category
Article
ISSN
0097-3165

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โœฆ Synopsis

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 F P , and we determine F P 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 supersolvable 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. 2001

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