cp's OEIS Frontend

A058129 Number of nonisomorphic monoids (semigroups with identity) of order n.

%I A058129 #51 Aug 11 2025 10:47:59
%S A058129 0,1,2,7,35,228,2237,31559,1668997,3685886630
%N A058129 Number of nonisomorphic monoids (semigroups with identity) of order n.
%H A058129 Geoff Cruttwell, <a href="https://www.reluctantm.com/gcruttw/publications/ams2014CruttwellCountingFiniteCats.pdf">Counting Finite Categories</a>, presentation, (2018).
%H A058129 Remigiusz Durka and Kamil Grela, <a href="https://arxiv.org/abs/1911.12814">On the number of possible resonant algebras</a>, arXiv:1911.12814 [hep-th], 2019.
%H A058129 Najwa Ghannoum, <a href="https://theses.hal.science/tel-03948327">Investigation of finite categories</a>, Doctoral thesis, Univ. Côte d'Azur (France); Univ. Libanaise (Lebanon), tel-0394832 [math.CT], 2022.
%H A058129 Pierre A. Grillet, <a href="https://doi.org/10.1080/00927872.2013.790036">Counting Semigroups</a>, Communications in Algebra, 43(2), 574-596, (2014).
%H A058129 Mikhail Kornev, <a href="https://arxiv.org/abs/2508.04454">On the Classification of n-Valued Monoids and Groups of Order 3</a>, arXiv:2508.04454 [math.GR], 2025. See p. 11.
%H A058129 Václav Koubek and Vojtěch Rödl, <a href="http://eudml.org/doc/17383">Note on the number of monoids of order n</a>, Commentationes Mathematicae Universitatis Carolinae 026.2 (1985): 309-314.
%H A058129 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 A058129 Clayton Cristiano Silva, <a href="http://www.ime.unicamp.br/~ftorres/ENSINO/MONOGRAFIAS/Clayton.pdf">Irreducible Numerical Semigroups</a>, University of Campinas, São Paulo, Brazil (2019).
%H A058129 <a href="/index/Mo#monoids">Index entries for sequences related to monoids</a>
%F A058129 a(n) = 2*A058133(n) - A058132(n).
%F A058129 a(n) < A027851(n) except for equality iff n = 1. - _M. F. Hasler_, Dec 10 2018
%F A058129 From _Elijah Beregovsky_, May 13 2025 (Start):
%F A058129 a(n) >= A027851(n-1).
%F A058129 Conjecture: a(n) = A027851(n-1)*(1+o(1)). See Koubek and Rödl paper in the Links.
%F A058129 Conjecture: a(n) = A058153(n)/n! * (1+o(1)). See Grillet paper in the Links. (End)
%Y A058129 Cf. A058132, A058133, A058153.
%Y A058129 Cf. A027851 (number of all nonisomorphic semigroups).
%K A058129 nonn,hard,more
%O A058129 0,3
%A A058129 _Christian G. Bower_, Nov 13 2000
%E A058129 a(8) from _Christian G. Bower_, Dec 26 2006
%E A058129 a(0) = 0 prepended by _M. F. Hasler_, Dec 10 2018
%E A058129 a(9) from _Elijah Beregovsky_, from the work of G. Cruttwell and R. Leblanc, May 12 2025