Flag-symmetry of the poset of shuffles and a local action of the symmetric group

Details Flag-symmetry of the poset of shuffles and a local action of the symmetric group Flag-symmetry of the poset of shuffles and a local action of the symmetric group

1998-06-10

arxiv.org/abs/math/9806057v1

Mathematics

Combinatorics

34 pages, 6 figures

Scientific paper

We show that the poset of shuffles introduced by Greene in 1988 is flag-symmetric, and we describe a "local" permutation action of the symmetric group on the maximal chains which is closely related to the flag symmetric function of the poset. A key tool is provided by a new labeling of the maximal chains of a poset of shuffles, which is also used to give bijective proofs of enumerative properties originally obtained by Greene. In addition we define a monoid of multiplicative functions on all posets of shuffles and describe this monoid in terms of a new operation on power series in two variables.

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