Home

The inverse semigroups of order <=15

The non-idempotent inverse semigroups of order <=15 up to isomorphism may be generated by the following Sage implementation of the algorithm in this paper.

Sage worksheet for generating the non-idempotent inverse semigroups of order <=15

Below are the Cayley tables for the non-idempotent inverse semigroups of order <=12. There is no guarantee that the Cayley tables generated by the above worksheet will be equal to or in the same order as the Cayley tables below. To obtain the Cayley tables for the idempotent inverse semigroups of order n, take the meet-semilattices of order n under the meet operation. (The meet-semilattices of order n are the lattices of order n+1 with the maximal element removed. The lattices of order <=15 are available here.)

I also have the Cayley tables for the non-idempotent inverse semigroups of order 13 and 14, although file size prevents me from posting them here. If you need them, please use the above Sage worksheet to generate them, or feel free to email me.

You will need to uncompress these files with a utility such as 7zip.

The non-idempotent inverse semigroups of order 2
The non-idempotent inverse semigroups of order 3
The non-idempotent inverse semigroups of order 4
The non-idempotent inverse semigroups of order 5
The non-idempotent inverse semigroups of order 6
The non-idempotent inverse semigroups of order 7
The non-idempotent inverse semigroups of order 8
The non-idempotent inverse semigroups of order 9
The non-idempotent inverse semigroups of order 10
The non-idempotent inverse semigroups of order 11
The non-idempotent inverse semigroups of order 12

Last updated June 11, 2015