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The symmetric group action on rank-selected posets of injective words (1606.03829v2)
Published 13 Jun 2016 in math.CO
Abstract: The symmetric group $\mathfrak{S}_n$ acts naturally on the poset of injective words over the alphabet ${1, 2,\dots,n}$. The induced representation on the homology of this poset has been computed by Reiner and Webb. We generalize their result by computing the representation of $\mathfrak{S}_n$ on the homology of all rank-selected subposets, in the sense of Stanley. A further generalization to the poset of $r$-colored injective words is given.