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The symmetric group Sn$\mathfrak {S}_{n}$ 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… Click to show full abstract
The symmetric group Sn$\mathfrak {S}_{n}$ 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 Sn$\mathfrak {S}_{n}$ 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.
Keywords:
injective words;
rank selected;
group action;
symmetric group
Journal Title: Order
Year Published: 2018
Link to full text (if available)
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Journal Title: Order
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!