Original entry on oeis.org
1, 3, 9, 36, 192, 1565, 19295, 878272, 1844953969, 52993098927711
Offset: 1
A058129
Number of nonisomorphic monoids (semigroups with identity) of order n.
Original entry on oeis.org
0, 1, 2, 7, 35, 228, 2237, 31559, 1668997, 3685886630
Offset: 0
- 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
Cf.
A027851 (number of all nonisomorphic semigroups).
a(9) from
Elijah Beregovsky, from the work of G. Cruttwell and R. Leblanc, May 12 2025
A058132
Number of self-converse monoids (semigroups with identity) of order n.
Original entry on oeis.org
0, 1, 2, 5, 19, 84, 509, 3901, 48957
Offset: 0
A151823
Number of nonequivalent monoids of order n with more than one invertible element.
Original entry on oeis.org
0, 1, 2, 9, 30, 213, 1757, 22956, 955569, 1853259264
Offset: 1
- Andreas Distler and Tom Kelsey, The Monoids of Order Eight and Nine, in: Intelligent Computer Mathematics, Lecture Notes in Computer Science, Volume 5144/2008, pp. 61-76, Springer-Verlag.
- Andreas Distler and Tom Kelsey, The Monoids of Orders Eight, Nine & Ten, Annals of Mathematics and Artificial Intelligence, 56 (2009), 3-25. [From Tom Kelsey (tom(AT)cs.st-and.ac.uk), Apr 01 2010]
Definition corrected by Tom Kelsey (tom(AT)cs.st-andrews.ac.uk), Apr 01 2010
Corrected and extended by Tom Kelsey (tom(AT)cs.st-and.ac.uk), Apr 01 2010
A058147
Triangle read by rows: number of monoids of order n with k idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
Original entry on oeis.org
1, 1, 1, 1, 3, 2, 2, 9, 10, 6, 1, 30, 47, 52, 26, 2, 175, 283, 413, 365, 135, 1, 3333, 2139, 3630, 4597, 3155, 875, 5
Offset: 1
1; 1,1; 1,3,2; 2,9,10,6; 1,30,47,52,26; ...
Original entry on oeis.org
1, 3, 10, 45, 273, 2510, 34069, 1703066
Offset: 1
Cf.
A001329,
A001423,
A001426,
A023814,
A027851,
A029851,
A058108,
A058132,
A058133,
A063756,
A079173,
A118581.
A176142
Number of nonequivalent monoids of order n in which the action of the unit group on the maximal ideal is nontrivial.
Original entry on oeis.org
0, 0, 0, 2, 5, 58, 428, 5539, 101082, 9269715
Offset: 1
A328746
Number of loops of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
Original entry on oeis.org
0, 1, 1, 1, 2, 5, 72, 12151, 53146457
Offset: 0
For the number of group-like algebraic structures of order n, see:
Showing 1-8 of 8 results.
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