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

1, 2, 13, 399, 55894

Offset: 0

Author

Geoffrey Critzer, Oct 17 2023

Keywords

• nonn
• more

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

Examples

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

Links

• 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.

Crossrefs

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