English

Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path

Rings and Algebras 2021-11-25 v1

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(Pn)IEnd(P_n) and PAut(Pn)PAut(P_n) of all injective partial endomorphisms and of all partial automorphisms of the undirected path PnP_n with nn vertices. We also describe Green's relations of PAut(Pn)PAut(P_n) and IEnd(Pn)IEnd(P_n) and calculate their cardinals.

Keywords

Cite

@article{arxiv.2101.12468,
  title  = {Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path},
  author = {Ilinka Dimitrova and Vítor H. Fernandes and Jörg Koppitz and Teresa M. Quinteiro},
  journal= {arXiv preprint arXiv:2101.12468},
  year   = {2021}
}
R2 v1 2026-06-23T22:38:58.763Z