A366722 Number of limit dominated binary relations on [n].

1, 2, 13, 399, 55894

Offset

0,2

Comments

A relation R is limit dominated iff R converges to a single limit L (A365534) and R is contained in L.

A convergent relation R is limit dominated iff the following implication holds for all x,y in [n]. If (x,y) is in R then there is a cyclic traverse from x to y in G(R), where G(R) is the directed graph with loops associated to R.

A relation R is limit dominated iff it converges to L, the smallest transitive relation (A006905) containing R. In which case, L is the union of R^i for all i >= 1. - Geoffrey Critzer, Dec 03 2023

Links

Table of n, a(n) for n=0..4.

D. A. Gregory, S. Kirkland, and N. J. Pullman, Power convergent Boolean matrices, Linear Algebra and its Applications, Volume 179, 15 January 1993, pp. 105-117.

D. Rosenblatt, On the graphs of finite Boolean relation matrices, Journal of Research of the National Bureau of Standards, 67B No. 4, 1963.

Example

Every idempotent relation (A121337) is limit dominated.
Every dense relation (A355730) is limit dominated.
Every primitive relation (A070322) is limit dominated.

Crossrefs

Cf. A365534, A121337, A006905, A366194, A355730, A070322.

Sequence in context: A336188 A348015 A131525 * A082751 A120935 A015183

Adjacent sequences: A366719 A366720 A366721 * A366723 A366724 A366725

Keyword

nonn,more

Author

Geoffrey Critzer, Oct 17 2023

Status

approved