Inverse Semigroups Data

This page contains the multiplication tables of the inverse semigroups of order at most 12. This data was originally make available by Martin E. Malandro on his webpage based on the method described in the paper:

Martin E. Malandro, ‘Enumeration of finite inverse semigroups’, preprint; https://arxiv.org/abs/1312.7192

The data was converted into a compressed format by Chris Russell. The tables in the linked files can be read into GAP using the function ReadMultiplicationTable in the Semigroups package version 3.1.0 or higher.

The files on this page are available gzipped and xzipped since the latter provides better compression in some cases.

The sequence of numbers of inverse semigroups up to isomorphism is A001428 on the OEIS.

inverse semigroup by order...

inverse semigroup of size 2 by number of idempotents...

inverse semigroup of size 3 by number of idempotents...

inverse semigroup of size 4 by number of idempotents...

inverse semigroup of size 5 by number of idempotents...

inverse semigroup of size 6 by number of idempotents...

inverse semigroup of size 7 by number of idempotents...

inverse semigroup of size 8 by number of idempotents...

inverse semigroup of size 9 by number of idempotents...

inverse semigroup of size 10 by number of idempotents...

inverse semigroup of size 11 by number of idempotents...

inverse semigroup of size 12 by number of idempotents...