cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A366194 #19 Dec 13 2023 08:18:04
%S A366194 1,2,13,177,4486
%N A366194 Number of limit dominating binary relations on [n].
%C A366194 A relation R is limit dominating iff R converges to a single limit L (A365534) and R contains L.  See Gregory, Kirkland, and Pullman.
%C A366194 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.
%C A366194 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
%H A366194 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, Pages 105-117.
%H A366194 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 A366194 Every idempotent relation (A121337) is limit dominating.
%e A366194 Every transitive relation (A006905) is limit dominating.
%e A366194 Every nilpotent relation (A003024) is limit dominating.
%Y A366194 Cf. A365534, A121337, A006905, A003024, A366722.
%K A366194 nonn,more
%O A366194 0,2
%A A366194 _Geoffrey Critzer_, Oct 03 2023