A058104 -id:A058104 - cp's OEIS frontend

A079175 Number of isomorphism classes of associative closed binary operations (semigroups) on a set of order n, listed by class size.

1, 1, 2, 3, 2, 0, 7, 15, 2, 0, 0, 7, 5, 0, 62, 112, 2, 0, 0, 0, 6, 0, 0, 8, 0, 2, 51, 0, 47, 2, 576, 1221, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 8, 0, 0, 4, 0, 48, 0, 0, 0, 0, 92, 0, 0, 42, 506, 0, 813, 32, 7397, 19684, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8

Offset: 0

Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

Elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)

			Triangle T(n,k) begins:
  1;
  1;
  2, 3;
  2, 0, 7, 15;
  2, 0, 0, 7, 5, 0, 62, 112;
  2, 0, 0, 0, 6, 0, 0, 8, 0, 2, 51, 0, 47, 2, 576, 1221;
  ...

Andrew Howroyd, Table of n, a(n) for n = 0..217 (rows 0..8; row 8 was derived from data given in the Distler-Kelsey reference)
C. van den Bosch, Closed binary operations on small sets
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

Row sums give A027851.

Cf. A023814, A027423 (row lengths), A079171, A079174, A079210.

A079174(n,k) + T(n,k) = A079171(n,k).
T(n, A027423(n)) = A058104(n).
A023814(n) = Sum_{k>=1} T(n,k)*A079210(n,k).

a(0)=1 prepended and terms a(16) and beyond from Andrew Howroyd, Jan 26 2022

A058113 Triangle: Number of asymmetric semigroups of order n with k idempotents.

Original entry on oeis.org

1, 2, 1, 3, 9, 3, 11, 37, 52, 12, 112, 224, 434, 383, 68, 4398, 1984, 3976, 5568, 3256, 502, 1181185, 47622, 44581, 74851, 74604, 31881, 4158

Offset: 1

Christian G. Bower, Nov 09 2000

			1; 2,1; 3,9,3; 11,37,52,12; 112,224,434,383,68; ...

Index entries for sequences related to semigroups

Row sums give A058104. Main diagonal: A058115. Column 1: A058114.

Updated Feb 19 2001

cp's OEIS Frontend

A079175 Number of isomorphism classes of associative closed binary operations (semigroups) on a set of order n, listed by class size.

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