cp's OEIS Frontend

A027851 Number of nonisomorphic semigroups of order n.

%I A027851 #57 Jul 03 2025 15:25:05
%S A027851 1,1,5,24,188,1915,28634,1627672,3684030417,105978177936292
%N A027851 Number of nonisomorphic semigroups of order n.
%H A027851 Özgur Akgun, Mun See Chang, Ian P. Gent, and Christopher Jefferson, <a href="https://arxiv.org/abs/2503.17251">Breaking the Symmetries of Indistinguishable Objects</a>, arXiv:2503.17251 [cs.AI], 2025. See pp. 14, 17.
%H A027851 Peter Cameron's Blog, <a href="https://cameroncounts.wordpress.com/2016/02/18/discrete-mathematics-and-big-data-summary/">The combinatorial explosion</a>, Posted 18/02/2016.
%H A027851 Andreas Distler, <a href="http://hdl.handle.net/10023/945">Classification and Enumeration of Finite Semigroups</a>, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).
%H A027851 A. Distler and T. Kelsey, <a href="http://arxiv.org/abs/1301.6023">The semigroups of order 9 and their automorphism groups</a>, arXiv preprint arXiv:1301.6023 [math.CO], 2013.
%H A027851 C. Noebauer, <a href="http://www.algebra.uni-linz.ac.at/~noebsi/">Home page</a>
%H A027851 C. Noebauer, <a href="ftp://www.algebra.uni-linz.ac.at/pub/noebauer/smallrings.ps.gz">The Numbers of Small Rings</a>
%H A027851 C. Noebauer, <a href="ftp://www.algebra.uni-linz.ac.at/pub/noebauer/thesis.ps.gz">Thesis on the enumeration of near-rings</a>
%H A027851 Eric Postpischil <a href="http://groups.google.com/groups?&amp;hl=en&amp;lr=&amp;ie=UTF-8&amp;selm=11802%40shlump.nac.dec.com&amp;rnum=2">Posting to sci.math newsgroup, May 21 1990</a>
%H A027851 Arman Shamsgovara, <a href="https://doi.org/10.1007/978-3-031-28083-2_14">Enumerating, Cataloguing and Classifying All Quantales on up to Nine Elements</a>, In: Glück, R., Santocanale, L., and Winter, M. (eds), Relational and Algebraic Methods in Computer Science (RAMiCS 2023) Lecture Notes in Computer Science, Springer, Cham, Vol. 13896.
%H A027851 Jeremy G. Sumner, Michael D. Woodhams, <a href="https://arxiv.org/abs/1709.00520">Lie-Markov models derived from finite semigroups</a>, arXiv:1709.00520 [math.GR], 2017.
%H A027851 Michael Torpey, <a href="https://doi.org/10.17630/10023-17350">Semigroup congruences: computational techniques and theoretical applications</a>, Ph.D. Thesis, University of St. Andrews (Scotland, 2019).
%H A027851 A. de Vries, <a href="http://haegar.fh-swf.de/Seminare/Genome/Archiv/languages.pdf">Formal Languages: An Introduction</a>, 2012.
%H A027851 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semigroup.html">Semigroup.</a>
%H A027851 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%F A027851 a(n) = A001423(n)*2 - A029851(n).
%F A027851 a(n) + A079173(n) = A001329(n).
%Y A027851 Cf. A001426, A023814, A058108.
%Y A027851 Cf. A001423, A029851, A079173, A001329.
%K A027851 nonn,hard,nice
%O A027851 0,3
%A A027851 _Christian G. Bower_, Dec 13 1997, updated Feb 19 2001
%E A027851 a(8)-a(9) from _Andreas Distler_, Jan 13 2011