Enumeration of finite inverse semigroups
Combinatorics
2019-12-25 v2 Group Theory
Rings and Algebras
Abstract
We give an efficient algorithm for the enumeration up to isomorphism of the inverse semigroups of order n, and we count the number S(n) of inverse semigroups of order n<=15. This improves considerably on the previous highest-known value S(9). We also give a related algorithm for the enumeration up to isomorphism of the finite inverse semigroups S with a given underlying semilattice of idempotents E, a given restriction of Green's D-relation on S to E, and a given list of maximal subgroups of S associated to the elements of E.
Keywords
Cite
@article{arxiv.1312.7192,
title = {Enumeration of finite inverse semigroups},
author = {Martin E. Malandro},
journal= {arXiv preprint arXiv:1312.7192},
year = {2019}
}
Comments
v2: Paper has been reorganized and rewritten for clarity and completeness. 31 pages, 16 tables