Involve: A Journal of Mathematics
- Volume 9, Number 3 (2016), 423-435.
Enumeration of $m$-endomorphisms
An -endomorphism on a free semigroup is an endomorphism that sends every generator to a word of length . Two -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 -endomorphisms on a rank- semigroup. From this formula, we derive several little-known integer sequences.
Involve, Volume 9, Number 3 (2016), 423-435.
Received: 6 February 2015
Revised: 14 July 2015
Accepted: 20 July 2015
First available in Project Euclid: 22 November 2017
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Rubin, Louis; Rushton, Brian. Enumeration of $m$-endomorphisms. Involve 9 (2016), no. 3, 423--435. doi:10.2140/involve.2016.9.423. https://projecteuclid.org/euclid.involve/1511371023