A007903 The number of distinct principal ideals in the semigroup of binary relations on an n-set.

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

Offset: 1

Author

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

Keywords

• nonn
• hard
• more
• nice

Comments

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

References

• K. H. Kim, Boolean Matrix Theory and Applications, Marcel Decker Inc., 1982.
• George Markowsky, 1991; Markowsky and Breen, 1993; Breen, 1995.

Links

• Jin Bai Kim, Tables of D-classes in the semigroup Bn of the binary relations on a set X with n-elements, Bull. Korean Math. Soc., Volume 20, Issue 1, 1983, pp. 9-13.
• Wikipedia, Green's relations
• Index entries for sequences related to semigroups

Crossrefs

Cf. A173311.

Formula

a(n) is asymptotic to 2^(n^2)/n!^2 (from Kim reference). - Geoffrey Critzer, May 14 2023