A001428 Number of inverse semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
1, 2, 5, 16, 52, 208, 911, 4637, 26422, 169163, 1198651, 9324047, 78860687, 719606005, 7035514642
Offset: 1
References
- S. Satoh, K. Yama, and 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]
Links
- Joao Araujo and 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).
- Luna Elliott, Alex Levine, and James Mitchell, E-disjunctive inverse semigroups, arXiv:2405.19825 [math.GR], 2024. See p. 3.
- 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
Crossrefs
Extensions
a(8) and a(9) from Andreas Distler, Jan 17 2011
Added more terms (from the Malandro reference), Joerg Arndt, Dec 30 2013