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The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations

Vladimir Ivanov, Sergei Kerov

Published 2003-02-18Version 1

We prove a convolution formula for the conjugacy classes in symmetric groups conjectured by the second author. A combinatorial interpretation of coefficients is provided. As a main tool we introduce new semigroup of partial permutations. We describe its structure, representations, and characters. We also discuss filtrations on the subalgebra of invariants in the semigroup algebra.

Comments: AMS-TeX, 19 pages, no figures
Journal: Journal of Mathematical Sciences (Kluwer) 107 (2001) no.5 4212-4230
Categories: math.CO, math.RT
Subjects: 05E10, 20B30, 20C30, 20C32, 20E45
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