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A001428 Number of inverse semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
(Formerly M1489 N0586)
1, 2, 5, 16, 52, 208, 911, 4637, 26422, 169163, 1198651, 9324047, 78860687, 719606005, 7035514642 (list; graph; refs; listen; history; text; internal format)



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

H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, Semigroup Forum, 14 (1977), 69-79.

R. J. Plemmons, Cayley Tables for All Semigroups of Order Less Than 7. Department of Mathematics, Auburn Univ., 1965.

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).

M. V. Lawson, Inverse Semigroups: The Theory of Partial Symmetries, World Scientific, 1998. [From Jonathan Vos Post, Mar 08 2010]

G. B. Preston, "Inverse semi-groups". Journal of the London Mathematical Society 29: 396-403. [From Jonathan Vos Post, Mar 08 2010]

V. V. Wagner (1952). "Generalised groups". Proceedings of the USSR Academy of Sciences 84: 1119-1122. (Russian) English translation. [From Jonathan Vos Post, Mar 08 2010]


Table of n, a(n) for n=1..15.

Joao Araujo, Michael Kinyon, An elegant 3-basis for inverse semigroups, March 21, 2010. [From Jonathan Vos Post, Mar 23 2010]

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

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

Martin E. Malandro, Enumeration of finite inverse semigroups, arXiv:1312.7192 [math.CO]

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

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)

Wikipedia, Inverse semigroup

Index entries for sequences related to semigroups


Cf. A234843 (commutative inverse semigroups), A234844 (inverse monoids), A234845 (commutative inverse monoids).

Sequence in context: A148394 A291685 A268571 * A055726 A101500 A268430

Adjacent sequences:  A001425 A001426 A001427 * A001429 A001430 A001431




N. J. A. Sloane.


a(8) and a(9) from Andreas Distler, Jan 17 2011

Added more terms (from the Malandro reference), Joerg Arndt, Dec 30 2013



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Last modified February 25 22:18 EST 2018. Contains 299662 sequences. (Running on oeis4.)