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arXiv · 2101.12468

Partial Automorphisms and Injective Partial 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 partial automorphisms and, more generally, injective partial endomorphisms of a finite undirected path from Semigroup Theory perspective. Our main objective is to give formulas for the ranks of the monoids $IEnd(P_n)$ and $PAut(P_n)$ of all injective partial endomorphisms and of all partial automorphisms of the undirected path $P_n$ with $n$ vertices. We also describe Green's relations of $PAut(P_n)$ and $IEnd(P_n)$ and calculate their cardinals.

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Ilinka Dimitrova, Vítor H. Fernandes, Jörg Koppitz, Teresa M. Quinteiro. 2021-01-29. Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path. https://doi.org/10.1007/s00233-021-10193-y

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