Enumeration of finite inverse semigroups
arXiv:1312.7192 · doi:10.1007/s00233-019-10054-9
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.
v2: Paper has been reorganized and rewritten for clarity and completeness. 31 pages, 16 tables