Enumeration of m-endomorphisms
Louis Rubin, Brian Rushton · Involve a Journal of Mathematics · 2016
An m-endomorphism on a free semigroup is an endomorphism that sends every generator to a word of length ≤ 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.