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arXiv · 1412.3001

Enumeration of m-Endomorphisms

Louis Rubin·Brian Rushton
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Abstract

An m-endomorphism of a free semigroup is an endomorphism that sends every generator to a word of length at most m. Two m-endomorphisms are combinatorially equivalent if they are conjugate under an automorphism of the semigroup. In this paper, we specialize an argument of N. G. de Bruijn to produce a formula for the number of combinatorial equivalence classes of m-endomorphisms on a rank-n semigroup. From this formula, we derive several little-known integer sequences.

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Louis Rubin, Brian Rushton. 2015-07-20. Enumeration of m-Endomorphisms. https://doi.org/10.2140/involve.2016.9.423

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