Enumeration of m-endomorphisms

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 03 Jun 2016Embargo end date: 01 Jan 2014 English Publisher:Mathematical Sciences PublishersJournal:Involve, a Journal of Mathematics, volume 9, pages 423-435 (issn: 1944-4176, eissn: 1944-4184,

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Authors: Rubin, Louis; Rushton, Brian;

doi: 10.2140/involve.2016.9.423 , 10.48550/arxiv.1412.3001

arXiv: 1412.3001

Enumeration of m-endomorphisms

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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.

To appear in Involve: A Journal of Mathematics

Related Organizations

University of Mary
United States
Brigham Young University Idaho
United States
Saint Louis University
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Keywords

Group Theory (math.GR), 05A99 (Primary), 20M15 (Secondary), enumeration, 20M15, semigroup, FOS: Mathematics, free semigroup endomorphisms, 05A99, Mathematics - Combinatorics, Combinatorics (math.CO), Mathematics - Group Theory

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