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The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations

Vladimir Ivanov·Sergei Kerov
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Abstract

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.

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Vladimir Ivanov, Sergei Kerov. 2003-02-18. The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations. https://arxiv.org/abs/math/0302203

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