The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations
Combinatorics
2007-05-23 v1 Representation Theory
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.
Cite
@article{arxiv.math/0302203,
title = {The Algebra of Conjugacy Classes in Symmetric Groups and Partial Permutations},
author = {Vladimir Ivanov and Sergei Kerov},
journal= {arXiv preprint arXiv:math/0302203},
year = {2007}
}
Comments
AMS-TeX, 19 pages, no figures