A058123 Triangle read by rows: semigroups of order n with k idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

1, 2, 2, 5, 7, 6, 19, 37, 44, 26, 132, 216, 351, 326, 135, 3107, 1780, 3093, 4157, 2961, 875, 623615, 32652, 33445, 53145, 56020, 30395, 6749, 1834861133, 4665709, 600027, 754315, 1007475, 822176, 348692, 60601, 52976551026562, 12710266442, 68769167, 14050493, 18660074, 20044250, 12889961, 4389418, 618111

Offset

1,2

Links

Andrey Zabolotskiy, Table of n, a(n) for n = 1..55 (rows 1-10)

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. Distler and T. Kelsey, The semigroups of order 9 and their automorphism groups, arXiv preprint arXiv:1301.6023 [math.CO], 2013.

Index entries for sequences related to semigroups

Example

Triangle starts:
    1;
    2,   2;
    5,   7,   6;
   19,  37,  44,  26;
  132, 216, 351, 326, 135;
  ...

Crossrefs

Row sums give A001423. Main diagonal: A002788. Columns 1-3: A002786, A002787, A005591.

Sequence in context: A023507 A095674 A207981 * A035586 A216392 A287908

Adjacent sequences: A058120 A058121 A058122 * A058124 A058125 A058126

Keyword

nonn,tabl,hard

Author

Christian G. Bower, Nov 10 2000

Extensions

More terms from Andreas Distler, Jan 13 2011

Status

approved