303 research outputs found
Flag-symmetry of the poset of shuffles and a local action of the symmetric group
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.Comment: 34 pages, 6 figure
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