cp's OEIS Frontend

A001428 Number of inverse semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

%I A001428 M1489 N0586 #47 Jun 03 2024 14:20:17
%S A001428 1,2,5,16,52,208,911,4637,26422,169163,1198651,9324047,78860687,
%T A001428 719606005,7035514642
%N A001428 Number of inverse semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
%D A001428 S. Satoh, K. Yama, and M. Tokizawa, Semigroups of order 8, Semigroup Forum 49 (1994), 7-29.
%D A001428 H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, Semigroup Forum, 14 (1977), 69-79.
%D A001428 R. J. Plemmons, Cayley Tables for All Semigroups of Order Less Than 7. Department of Mathematics, Auburn Univ., 1965.
%D A001428 R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.
%D A001428 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001428 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A001428 M. V. Lawson, Inverse Semigroups: The Theory of Partial Symmetries, World Scientific, 1998. [From _Jonathan Vos Post_, Mar 08 2010]
%D A001428 G. B. Preston, "Inverse semi-groups". Journal of the London Mathematical Society 29: 396-403. [From _Jonathan Vos Post_, Mar 08 2010]
%D A001428 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]
%H A001428 Joao Araujo and Michael Kinyon, <a href="http://arxiv.org/abs/1003.4028">An elegant 3-basis for inverse semigroups</a>, March 21, 2010. [From _Jonathan Vos Post_, Mar 23 2010]
%H A001428 Andreas Distler, <a href="http://hdl.handle.net/10023/945">Classification and Enumeration of Finite Semigroups</a>, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).
%H A001428 Luna Elliott, Alex Levine, and James Mitchell, <a href="https://arxiv.org/abs/2405.19825">E-disjunctive inverse semigroups</a>, arXiv:2405.19825 [math.GR], 2024. See p. 3.
%H A001428 H. Juergensen and P. Wick, <a href="/A001423/a001423.pdf">Die Halbgruppen von Ordnungen <= 7</a>, annotated and scanned copy.
%H A001428 Martin E. Malandro, <a href="http://arxiv.org/abs/1312.7192">Enumeration of finite inverse semigroups</a>, arXiv:1312.7192 [math.CO]
%H A001428 R. J. Plemmons, <a href="/A001423/a001423_2.pdf">There are 15973 semigroups of order 6</a> (annotated and scanned copy)
%H A001428 N. J. A. Sloane, <a href="/A001329/a001329.jpg">Overview of A001329, A001423-A001428, A258719, A258720.</a>
%H A001428 T. Tamura, <a href="/A001329/a001329.pdf">Some contributions of computation to semigroups and groupoids</a>, pp. 229-261 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970. (Annotated and scanned copy)
%H A001428 Wikipedia, <a href="https://en.wikipedia.org/wiki/Inverse_semigroup">Inverse semigroup</a>
%H A001428 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%Y A001428 Cf. A234843 (commutative inverse semigroups), A234844 (inverse monoids), A234845 (commutative inverse monoids).
%K A001428 nonn,nice,hard,more
%O A001428 1,2
%A A001428 _N. J. A. Sloane_
%E A001428 a(8) and a(9) from _Andreas Distler_, Jan 17 2011
%E A001428 Added more terms (from the Malandro reference), _Joerg Arndt_, Dec 30 2013