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arXiv · 1606.03829

The symmetric group action on rank-selected posets of injective words

Christos A. Athanasiadis
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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.

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Christos A. Athanasiadis. 2016-10-27. The symmetric group action on rank-selected posets of injective words. https://arxiv.org/abs/1606.03829

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