A002787 Number of semigroups of order n with 2 idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator). (Formerly M1802 N0712)

2, 7, 37, 216, 1780, 32652, 4665709, 12710266442, 381279977009776

Offset

2,1

References

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

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).

Links

Table of n, a(n) for n=2..10.

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

Andreas Distler, Chris Jefferson, Tom Kelsey, Lars Kotthoff, The Semigroups of Order 10, in: M. Milano (Ed.), Principles and Practice of Constraint Programming, 18th International Conference, CP 2012, Québec City, QC, Canada, October 8-12, 2012, Proceedings (LNCS, volume 7514), pp. 883-899, Springer-Verlag Berlin Heidelberg 2012. a(10) is the Table 3 Total.

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

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

Column 2 of A058123.

Sequence in context: A041051 A175487 A216362 * A062394 A245902 A063766

Adjacent sequences: A002784 A002785 A002786 * A002788 A002789 A002790

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Extensions

a(8)-a(9) from Andreas Distler, Jan 13 2011

a(10) from Andrey Zabolotskiy, Nov 08 2018

Status

approved