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

1,1

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

Table of n, a(n) for n=1..7.

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

Formula

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

Crossrefs

Cf. A173311.

Sequence in context: A173312 A351184 A156434 * A182100 A327484 A006894

Adjacent sequences: A007900 A007901 A007902 * A007904 A007905 A007906

Keyword

nonn,hard,more,nice

Author

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

Status

approved