From: buck@shuksan.math.niu.edu (J. B. Stephen (Buck))
Newsgroups: sci.math
Subject: Re: Number of semigroups of order n
Date: 9 Apr 1998 16:09:11 GMT
There has been some work on this.
The cases up to 6 are classic (from the 50's)
I think Nakamura (?).
I don't have my books here, but a good start
may be Clifford and Preston's "Semigroup Theory"
(Vol. 1, from the American Mathematical Society).
Additionally, Light's associativity test is
discussed there. This may help you, but
you've probably come up with it yourself.
Note that it is standard practice to enumerate these
things up to isomorphism and anti-isomorphism.
Buck
In article <6ggk32$jpt@sv074.SanDiegoCA.NCR.COM>,
Joseph Riel wrote:
>How may semigroups are there of order n?
>That is, given all nxn cayley tables, how many are associative?