A002786 Semigroups of order n with 1 idempotent, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
1, 2, 5, 19, 132, 3107, 623615, 1834861133, 52976551026562, 12417619575092896741
Offset: 1
References
- 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
- 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 sum of entries of Tables 4 and 5; note that Table 4 has incorrect Total.
- H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, Semigroup Forum, 14 (1977), 69-79.
- 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 1 of A058123.
Extensions
a(8)-a(9) from Andreas Distler, Jan 13 2011
a(10) from Andrey Zabolotskiy, Nov 08 2018