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arXiv · 1810.09307

Ranks of monoids of endomorphisms of a finite undirected path

Ilinka Dimitrova·Vítor H. Fernandes·Jörg Koppitz·Teresa M. Quinteiro
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Abstract

In this paper we study the widely considered endomorphisms and weak endomorphisms of a finite undirected path from monoid generators perspective. Our main aim is to determine the ranks of the monoids $wEnd P_n$ and $End P_n$ of all weak endomorphisms and all endomorphisms of the undirected path $P_n$ with $n$ vertices. We also consider strong and strong weak endomorphisms of $P_n$.

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Ilinka Dimitrova, Vítor H. Fernandes, Jörg Koppitz, Teresa M. Quinteiro. 2018-10-22. Ranks of monoids of endomorphisms of a finite undirected path. https://doi.org/10.1007/s40840-019-00762-4

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