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A001423 Number of semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
(Formerly M3550 N1438)
1, 1, 4, 18, 126, 1160, 15973, 836021, 1843120128, 52989400714478 (list; graph; refs; listen; history; text; internal format)



A. de Vries, Formal Languages: An Introduction, http://haegar.fh-swf.de/Seminare/Genome/Archiv/languages.pdf

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]

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.

D. J. Kleitman, B. L. Rothschild and J. 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, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.

Satoh, S.; Yama, K.; and Tokizawa, M., Semigroups of order 8, Semigroup Forum 49 (1994), 7-29.

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).


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

Andreas Distler, Classification and Enumeration of Finite Semigroups, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).

A. Distler and T. Kelsey, The semigroups of order 9 and their automorphism groups, arXiv preprint arXiv:1301.6023, 2013.

H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, annotated and scanned copy.

R. J. Plemmons, There are 15973 semigroups of order 6 (annotated and scanned copy)

Eric Postpischil Posting to sci.math newsgroup, May 21 1990

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


a(n)=(A027851(n)+A029851(n))/2. Cf. A001426, A023814, A058107, A058123, A151823.

Sequence in context: A215691 A073511 A108704 * A158341 A144272 A034517

Adjacent sequences:  A001420 A001421 A001422 * A001424 A001425 A001426




N. J. A. Sloane.


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



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Last modified October 25 13:22 EDT 2016. Contains 277127 sequences.