Enumeration of m-Endomorphisms
Combinatorics
2016-06-08 v9 Group Theory
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.
Cite
@article{arxiv.1412.3001,
title = {Enumeration of m-Endomorphisms},
author = {Louis Rubin and Brian Rushton},
journal= {arXiv preprint arXiv:1412.3001},
year = {2016}
}
Comments
To appear in Involve: A Journal of Mathematics