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

1, 2, 13, 177, 4486

Offset: 0

Author

Geoffrey Critzer, Oct 03 2023

Keywords

• nonn
• more

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

Examples

			Every idempotent relation (A121337) is limit dominating.
Every transitive relation (A006905) is limit dominating.
Every nilpotent relation (A003024) is limit dominating.
		

Links

• 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.

Crossrefs

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