@article{cb0802f4268443e5bf6aef622c340347,
title = "Partial automorphisms and injective partial endomorphisms of a finite undirected path",
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) and PAut (Pn) of all injective partial endomorphisms and of all partial automorphisms of the undirected path Pn with n vertices. We also describe Green{\textquoteright}s relations of PAut (Pn) and IEnd (Pn) and calculate their cardinals.",
keywords = "Generators, Injective partial endomorphisms, Partial automorphisms, Paths, Rank",
author = "I. Dimitrova and Fernandes, {V{\'i}tor Hugo} and J. Koppitz and Quinteiro, {Teresa Maria}",
note = "Funding Information: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT# Funding Information: This work was produced, in part, during the visit of the first and third authors to CMA, FCT NOVA, Lisbon, in July 2019. The first author was supported by CMA through a visiting researcher fellowship. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2021",
month = aug,
doi = "10.1007/s00233-021-10193-y",
language = "English",
volume = "103",
pages = "87--105",
journal = "Semigroup Forum",
issn = "0037-1912",
publisher = "Springer",
number = "1",
}