

A001428


Number of inverse semigroups of order n, considered to be equivalent when they are isomorphic or antiisomorphic (by reversal of the operator).
(Formerly M1489 N0586)


13



1, 2, 5, 16, 52, 208, 911, 4637, 26422, 169163, 1198651, 9324047, 78860687, 719606005, 7035514642
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OFFSET

1,2


REFERENCES

S. Satoh, K. Yama, M. Tokizawa, Semigroups of order 8, Semigroup Forum 49 (1994), 729.
H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, Semigroup Forum, 14 (1977), 6979.
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), 217; 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 semigroups". Journal of the London Mathematical Society 29: 396403. [From Jonathan Vos Post, Mar 08 2010]
V. V. Wagner (1952). "Generalised groups". Proceedings of the USSR Academy of Sciences 84: 11191122. (Russian) English translation. [From Jonathan Vos Post, Mar 08 2010]


LINKS

Table of n, a(n) for n=1..15.
Joao Araujo, Michael Kinyon, An elegant 3basis 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, A001423A001428, A258719, A258720.
T. Tamura, Some contributions of computation to semigroups and groupoids, pp. 229261 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


CROSSREFS

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


KEYWORD

nonn,nice,hard,more


AUTHOR

N. J. A. Sloane.


EXTENSIONS

a(8) and a(9) from Andreas Distler, Jan 17 2011
Added more terms (from the Malandro reference), Joerg Arndt, Dec 30 2013


STATUS

approved



