Groupoids have entered the OEIS !

[franktaw at netscape.net]

Umm, you should know that the word "groupoid" has multiple meanings.  
And
(one of) the other one(s) is already in the OEIS.  See A001424 and 
A001329,
or take a look at http://mathworld.wolfram.com/Groupoid.html.

In addition to the meanings there, I think I have seen it used for a 
set with a
binary operation which is solvable and cancellable (equivalent 
conditions for
finite examples), but not necessarily associative.  In other words, the 
operation
table is a Latin square.  These are also called quasigroups, or 
sometimes loops.

Franklin T. Adams-Watters

-----Original Message-----
From: Benoît Jubin <benoit.jubin at gmail.com>

Dear SeqFans,

I have just contributed six sequences counting finite groupoids
(categories all of whose morphisms are invertible):
- A140185 (connected groupoids with n morphisms)
- A140186 (connected groupoids with n more morphisms than objects)
- A140187 (connected groupoids with n times as many morphisms as 
objects)
- A140188 (groupoids with n morphisms and k objects)
- A140189 (groupoids with n morphisms)
- A140190 (groupoids with m morphisms and (m-n) objects for any m>=2n)
The difficulty of counting groupoids is almost entirely in the
counting of groups, so that these sequences are not hard to compute
from A000001.

Maybe this is worth a new entry in the OEIS index ? (and by the way,
another entry for categories could be added):
categories: A125696, A125697, A125701
categories, connected: A125698, A125699, A125700, A125702
categories, strongly connected: [sequences to be added]
groupoids (categories with inverses): A140188, A140189, A140190
groupoids (categories with inverses), connected: A140185, A140186, 
A140187

For the curious, here are two surveys on groupoids:
- Ronald Brown, From groups to groupoids: a brief survey
http://www.bangor.ac.uk/~mas010/groupoidsurvey.pdf
- Alan Weinstein, Groupoids: unifying internal and external symmetry
http://www.ams.org/notices/199607/weinstein.pdf

Sincerely,
Benoit Jubin
[my oeis page: math.berkeley.edu/~jubin/oeis.html ]