A002788 Idempotent semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

1, 1, 2, 6, 26, 135, 875, 6749, 60601, 618111, 7033090

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• hard

Comments

An idempotent semigroup is one whose elements are all idempotents.

References

• R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.
• R. J. Plemmons, Construction and analysis of non-equivalent finite semigroups, pp. 223-228 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.
• S. Satoh, K. Yama and M. Tokizawa, Semigroups of order 8; Semigroup Forum 49, 1994.
• 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).

Links

• Andreas Distler, Classification and Enumeration of Finite Semigroups, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).
• R. J. Plemmons, There are 15973 semigroups of order 6 (annotated and scanned copy)
• Eric Weisstein's World of Mathematics, Semigroup.
• Index entries for sequences related to semigroups

Crossrefs

Cf. A001423. Main diagonal of A058123.

Extensions

Additional reference and comments from Michael Somos

a(7) term from Christian G. Bower, Feb 19 2001

a(8) (from the Satoh et al. reference) sent by Tom Kelsey (tom(AT)cs.st-and.ac.uk), Jun 17 2008

a(9)-a(10) from Andreas Distler, Jan 12 2011