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

0, 1, 2, 7, 35, 228, 2237, 31559, 1668997, 3685886630

Offset

0,3

Links

Table of n, a(n) for n=0..9.

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).

Nicholas Johnston, Edmond W. H. Lee, and Vehbi E. Paksoy, Uniqueness of the smallest chameleon in the class of monoids, Examples and Counterexamples (2025) Vol. 8, Art. 100209.

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) = 2*A058133(n) - A058132(n).

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)

Crossrefs

Cf. A058132, A058133, A058153.

Cf. A027851 (number of all nonisomorphic semigroups).

Sequence in context: A014307 A000154 A003713 * A101514 A380843 A247240

Adjacent sequences: A058126 A058127 A058128 * A058130 A058131 A058132

Keyword

nonn,hard,more

Author

Christian G. Bower, Nov 13 2000

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

Status

approved