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.

A358784 Size of largest semigroup generated by three n X n boolean matrices.

This page as a plain text file.
%I A358784 #5 Nov 30 2022 07:17:13
%S A358784 2,16,440
%N A358784 Size of largest semigroup generated by three n X n boolean matrices.
%C A358784 Here the semigroup is under boolean matrix multiplication (not the same as GF(2) matrix multiplication).  It is known that a(4) >= 24846, generated by the three matrices [[0,0,0,1],[1,0,0,0],[0,1,0,0],[0,0,1,0]] and [[0,0,0,1],[0,0,1,0],[0,1,0,0],[1,0,0,1]] and [[0,0,0,0],[0,0,0,1],[0,0,1,0],[0,1,0,0]].
%e A358784 For n = 1 the maximum size is 2, generated by the three matrices [0] and [1] and [1].
%e A358784 For n = 2 the maximum size is 16, generated by the three matrices [[0,1],[1,1]] and [[0,1],[1,0]] and [[0,0],[0,1]].
%e A358784 For n = 3 the maximum size is 440, generated by the three matrices [[0,0,1],[1,0,0],[0,1,0]] and [[0,0,1],[0,1,0],[1,0,1]] and [[0,0,0],[0,0,1],[0,1,0]].
%Y A358784 Cf. A217990 (for one matrix); A202140 (for two matrices).
%K A358784 nonn,hard,more,bref
%O A358784 1,1
%A A358784 _Jeffrey Shallit_, Nov 30 2022