A representation on the labeled rooted forests
classification
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math.CO
keywords
grouprepresentationsymmetricactionaffordapplicationscharacterconjugation
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We consider conjugation action of symmetric group on the semigroup of all partial functions and develop a machinery to investigate character formulas and multiplicities. In particular, we determine nilpotent matrices whose orbit under symmetric group afford the sign representation. Applications to rook theory are offered.
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