The Symmetric Group Action on Rank-selected Posets of Injective Words
Tóm tắt
The symmetric group
$\mathfrak {S}_{n}$
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
$\mathfrak {S}_{n}$
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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