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A366722
Number of limit dominated binary relations on [n].
2
1, 2, 13, 399, 55894
OFFSET
0,2
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
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.
EXAMPLE
Every idempotent relation (A121337) is limit dominated.
Every dense relation (A355730) is limit dominated.
Every primitive relation (A070322) is limit dominated.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Geoffrey Critzer, Oct 17 2023
STATUS
approved