A001423 Number of semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

1, 1, 4, 18, 126, 1160, 15973, 836021, 1843120128, 52989400714478, 12418001077381302684

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more
• nice

References

• David Nacin, "Puzzles, Parity Maps, and Plenty of Solutions", Chapter 15, The Mathematics of Various Entertaining Subjects: Volume 3 (2019), Jennifer Beineke & Jason Rosenhouse, eds. Princeton University Press, Princeton and Oxford, p. 245.
• R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• A. de Vries, Formal Languages: An Introduction
• Andreas Distler, Classification and Enumeration of Finite Semigroups, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).
• Andreas Distler and Tom Kelsey, The Monoids of Order Eight and Nine, in Intelligent Computer Mathematics, Lecture Notes in Computer Science, Volume 5144/2008, Springer-Verlag. [From _N. J. A. Sloane_, Jul 10 2009]
• A. Distler and T. Kelsey, The semigroups of order 9 and their automorphism groups, arXiv preprint arXiv:1301.6023 [math.CO], 2013.
• Andreas Distler, Chris Jefferson, Tom Kelsey, and Lars Kotthoff, The Semigroups of Order 10, in: M. Milano (Ed.), Principles and Practice of Constraint Programming, 18th International Conference, CP 2012, Québec City, QC, Canada, October 8-12, 2012, Proceedings (LNCS, volume 7514), pp. 883-899, Springer-Verlag Berlin Heidelberg 2012.
• Remigiusz Durka and Kamil Grela, On the number of possible resonant algebras, arXiv:1911.12814 [hep-th], 2019.
• G. E. Forsythe, SWAC computes 126 distinct semigroups of order 4, Proc. Amer. Math. Soc. 6, (1955). 443-447.
• H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, Semigroup Forum, 14 (1977), 69-79.
• H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, annotated and scanned copy.
• Daniel J. Kleitman, Bruce L. Rothschild and Joel H. Spencer, The number of semigroups of order n, Proc. Amer. Math. Soc., 55 (1976), 227-232.
• R. J. Plemmons, There are 15973 semigroups of order 6 (annotated and scanned copy)
• Eric Postpischil Associativity Problem, Posting to sci.math newsgroup, May 21 1990.
• S. Satoh, K. Yama, and M. Tokizawa, Semigroups of order 8, Semigroup Forum 49 (1994), 7-29.
• N. J. A. Sloane, Overview of A001329, A001423-A001428, A258719, A258720.
• T. Tamura, Some contributions of computation to semigroups and groupoids, pp. 229-261 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970. (Annotated and scanned copy)
• Eric Weisstein's World of Mathematics, Semigroup.
• Index entries for sequences related to semigroups

Crossrefs

Cf. A001426, A023814, A058107, A058123, A151823.

Formula

a(n) = (A027851(n) + A029851(n))/2.

Extensions

a(9) added by Andreas Distler, Jan 12 2011

a(10) from Distler et al. 2012, added by Andrey Zabolotskiy, Nov 08 2018