Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path

Ilinka Dimitrova; Vítor H. Fernandes; Jörg Koppitz; Teresa M. Quinteiro

doi:10.1007/s00233-021-10193-y

paper

Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path

arXiv:2101.12468 · doi:10.1007/s00233-021-10193-y

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 $I E n d (P_{n})$ and $P A u t (P_{n})$ 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 $P A u t (P_{n})$ and $I E n d (P_{n})$ and calculate their cardinals.

References in corpus (1)

Ranks of monoids of endomorphisms of a finite undirected path