A366722 - OEIS

%I #24 Dec 13 2023 08:34:33

%S 1,2,13,399,55894

%N Number of limit dominated binary relations on [n].

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

%C 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.

%C 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

%H D. A. Gregory, S. Kirkland, and N. J. Pullman, <a href="https://doi.org/10.1016/0024-3795(93)90323-G">Power convergent Boolean matrices</a>, Linear Algebra and its Applications, Volume 179, 15 January 1993, pp. 105-117.

%H D. Rosenblatt, <a href="https://nvlpubs.nist.gov/nistpubs/jres/67B/jresv67Bn4p249_A1b.pdf">On the graphs of finite Boolean relation matrices</a>, Journal of Research of the National Bureau of Standards, 67B No. 4, 1963.

%e Every idempotent relation (A121337) is limit dominated.

%e Every dense relation (A355730) is limit dominated.

%e Every primitive relation (A070322) is limit dominated.

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

%K nonn,more

%O 0,2

%A _Geoffrey Critzer_, Oct 17 2023