The Symmetric Group Action on Rank-selected Posets of Injective Words

نویسنده

Christos A. Athanasiadis

چکیده

The symmetric group Sn 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 Sn 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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