Add inverse semigroups

[james-d-mitchell]

The paper:

https://arxiv.org/abs/1312.7192

describes how to obtain the inverse semigroups of order up to 15, and until recently data files were available at:

https://www.shsu.edu/mem037/ISGs.html

They are still available via the internet archive at:

https://web.archive.org/web/20230320051235/https://www.shsu.edu/mem037/ISGs.html

and

https://web.archive.org/web/20230405135645/https://www.shsu.edu/mem037/Lattices.html

At some point in the past year or so I stored the multiplication tables for the inverse semigroups of order at most 12 in the following files (which can be read into GAP using ReadMultiplicationTable from the Semigroups package):

cay-2.gz
cay-3.gz
cay-4.gz
cay-5.gz
cay-6.gz
cay-7.gz
cay-8.gz
cay-9.gz
cay-10.gz
cay-11.gz

The file for 12 is too big to upload here.

[wilfwilson]

Nice idea!

[mtorpey]

@DanielPointon is working on this now!

[james-d-mitchell]

From the webpage of the creator: https://profiles.shsu.edu/mem037/Lattices.html

The unlabeled lattices on 15 or fewer nodes, up to isomorphism, are given in the following files as lists of cover relations. Each line of each file is the list of cover relations for a single lattice, and the cover relation [a,b] means b covers a. These files were generated with a Sage implementation of the algorithm of Heitzig and Reinhold.

In these files, the nodes of the lattices of order n are the integers from 0 to n-1. In each of these lattices 0 is the minimal element and 1 is the maximal element.

The linked files are:

Lattice Cover Relations 9.txt.gz
Lattice Cover Relations 10.txt.gz
Lattice Cover Relations 11.txt.gz
Lattice Cover Relations 12.txt.gz
Lattice Cover Relations 13.txt.gz

The link on https://profiles.shsu.edu/mem037/Lattices.html to the lattices of size 15 is broken, and the file for n = 14 is too large to upload here (130mb vs the 25mb limit)

[james-d-mitchell]

Just to say that I've been in touch with Martin Malandro and he has been kind enough to upload the other files that he has for lattices of size 15, and non-semilattice inverse semigroups of sizes 13 and 14. I have downloaded those files, but they can also be downloaded directly at:

https://profiles.shsu.edu/mem037/Lattices.html
https://profiles.shsu.edu/mem037/ISGs.html

Thanks to Martin!

[DanielPointon]

I've made some progress on this issue (made some functions to serialise a multiplication table so it can be written to file), in theory that's at least half way there when coupled with ReadMultiplicationTable, but I wasn't able to get any further before the VIP ended. I've documented the progress I made in the draft pull request above