The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66551We 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.AMS-TeX, 19 pages, no figuresCombinatoricsRepresentation Theory05E10 (Primary) 20B30, 20C30, 20C32, 20E45 (Secondary)The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutationstext