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Enumeration of
$m$-endomorphisms
Louis Rubin and Brian Rushton
Vol. 9 (2016), No. 3, 423–435
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Abstract |
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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. |
Keywords
enumeration, free semigroup endomorphisms, semigroup
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Mathematical Subject Classification 2010
Primary: 05A99
Secondary: 20M15
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Milestones
Received: 6 February 2015
Revised: 14 July 2015
Accepted: 20 July 2015
Published: 3 June 2016
Communicated by Vadim Ponomarenko
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Authors |
| Louis Rubin | |
| Department of Mathematics and
Computer Science St. Louis University 220 North Grand Boulevard St. Louis, MO 63103 United States |
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| Brian Rushton | |
| Department of Mathematics Brigham Young University 268 TMCB Provo, UT 84602 United States |
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