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## 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*