Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 3 (2016), 423-435.

Enumeration of $m$-endomorphisms

Louis Rubin and Brian Rushton

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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.

Article information

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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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05A99: None of the above, but in this section
Secondary: 20M15: Mappings of semigroups

enumeration free semigroup endomorphisms semigroup


Rubin, Louis; Rushton, Brian. Enumeration of $m$-endomorphisms. Involve 9 (2016), no. 3, 423--435. doi:10.2140/involve.2016.9.423.

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