A058129 Number of nonisomorphic monoids (semigroups with identity) of order n.
0, 1, 2, 7, 35, 228, 2237, 31559, 1668997, 3685886630
Offset: 0
Links
- Geoff Cruttwell, Counting Finite Categories, presentation, (2018).
- Remigiusz Durka and Kamil Grela, On the number of possible resonant algebras, arXiv:1911.12814 [hep-th], 2019.
- Najwa Ghannoum, Investigation of finite categories, Doctoral thesis, Univ. Côte d'Azur (France); Univ. Libanaise (Lebanon), tel-0394832 [math.CT], 2022.
- Pierre A. Grillet, Counting Semigroups, Communications in Algebra, 43(2), 574-596, (2014).
- Mikhail Kornev, On the Classification of n-Valued Monoids and Groups of Order 3, arXiv:2508.04454 [math.GR], 2025. See p. 11.
- Václav Koubek and Vojtěch Rödl, Note on the number of monoids of order n, Commentationes Mathematicae Universitatis Carolinae 026.2 (1985): 309-314.
- Eric Postpischil, Posting to sci.math newsgroup, May 21 1990
- Clayton Cristiano Silva, Irreducible Numerical Semigroups, University of Campinas, São Paulo, Brazil (2019).
- Index entries for sequences related to monoids
Formula
a(n) < A027851(n) except for equality iff n = 1. - M. F. Hasler, Dec 10 2018
From Elijah Beregovsky, May 13 2025 (Start):
a(n) >= A027851(n-1).
Conjecture: a(n) = A027851(n-1)*(1+o(1)). See Koubek and Rödl paper in the Links.
Conjecture: a(n) = A058153(n)/n! * (1+o(1)). See Grillet paper in the Links. (End)
Extensions
a(8) from Christian G. Bower, Dec 26 2006
a(0) = 0 prepended by M. F. Hasler, Dec 10 2018
a(9) from Elijah Beregovsky, from the work of G. Cruttwell and R. Leblanc, May 12 2025