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

Original entry on oeis.org

2, 16, 440
Offset: 1

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Author

Jeffrey Shallit, Nov 30 2022

Keywords

Comments

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]].

Examples

			For n = 1 the maximum size is 2, generated by the three matrices [0] and [1] and [1].
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]].
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]].

Crossrefs

Cf. A217990 (for one matrix); A202140 (for two matrices).
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