Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Tome 256 (1999), pp. 95-120
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V. N. Ivanov; S. V. Kerov. The algebra of conjugacy classes in symmetric groups, and partial permutations. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part III, Tome 256 (1999), pp. 95-120. http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a7/
@article{ZNSL_1999_256_a7,
author = {V. N. Ivanov and S. V. Kerov},
title = {The algebra of conjugacy classes in symmetric groups, and partial permutations},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {95--120},
year = {1999},
volume = {256},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a7/}
}
TY - JOUR
AU - V. N. Ivanov
AU - S. V. Kerov
TI - The algebra of conjugacy classes in symmetric groups, and partial permutations
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1999
SP - 95
EP - 120
VL - 256
UR - http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a7/
LA - ru
ID - ZNSL_1999_256_a7
ER -
%0 Journal Article
%A V. N. Ivanov
%A S. V. Kerov
%T The algebra of conjugacy classes in symmetric groups, and partial permutations
%J Zapiski Nauchnykh Seminarov POMI
%D 1999
%P 95-120
%V 256
%U http://geodesic.mathdoc.fr/item/ZNSL_1999_256_a7/
%G ru
%F ZNSL_1999_256_a7
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.
