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

2016/06/13 by Athanasiadis, Christos A.
#05E18 #20C30 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.03829

Abstract

The symmetric group \mathfrakS_n acts naturally on the poset of injective words over the alphabet \1, 2,…,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 \mathfrakS_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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