A007903 - OEIS

%I #44 Jun 01 2023 13:57:50

%S 2,4,11,60,877,42944,7339704

%N The number of distinct principal ideals in the semigroup of binary relations on an n-set.

%C a(n) is the number of Green's J-classes in the semigroup of binary relations on an n-set. - _James Mitchell_, May 10 2015

%D K. H. Kim, Boolean Matrix Theory and Applications, Marcel Decker Inc., 1982.

%D George Markowsky, 1991; Markowsky and Breen, 1993; Breen, 1995.

%H Jin Bai Kim, <a href="http://www.koreascience.or.kr/article/JAKO198311919478487.page">Tables of D-classes in the semigroup Bn of the binary relations on a set X with n-elements</a>, Bull. Korean Math. Soc., Volume 20, Issue 1, 1983, pp. 9-13.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Green%27s_relations">Green's relations</a>

%H <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>

%F a(n) is asymptotic to 2^(n^2)/n!^2 (from Kim reference). - _Geoffrey Critzer_, May 14 2023

%Y Cf. A173311.

%K nonn,hard,more,nice

%O 1,1

%A Michael A Breen (MAB1699(AT)tntech.edu)