A representation on the labeled rooted forests |
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Authors: | Mahir Bilen Can |
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Institution: | Department of Mathematics, Tulane University, New Orleans, USA |
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Abstract: | We consider the conjugation action of symmetric group on the semigroup of all partial functions and develop a machinery to investigate character formulas and multiplicities. By interpreting these objects in terms of labeled rooted forests, we give a characterization of the labeled rooted trees whose Sn orbit afford the sign representation. Applications to rook theory are offered. |
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Keywords: | Labeled rooted trees nilpotent partial transformations plethysm symmetric group |
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