A366194 Number of limit dominating binary relations on [n].

1, 2, 13, 177, 4486

Offset

0,2

Comments

A relation R is limit dominating iff R converges to a single limit L (A365534) and R contains L. See Gregory, Kirkland, and Pullman.

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

A relation R is limit dominating iff it converges to L, the biggest dense relation (A355730) contained in R. In which case L is the intersection 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, Pages 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 dominating.
Every transitive relation (A006905) is limit dominating.
Every nilpotent relation (A003024) is limit dominating.

Crossrefs

Cf. A365534, A121337, A006905, A003024, A366722.

Sequence in context: A182314 A268988 A183606 * A307655 A137610 A073178

Adjacent sequences: A366191 A366192 A366193 * A366195 A366196 A366197

Keyword

nonn,more

Author

Geoffrey Critzer, Oct 03 2023

Status

approved