<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Dimitrova, I.</style></author><author><style face="normal" font="default" size="100%">Fernandes, Vítor H.</style></author><author><style face="normal" font="default" size="100%">Koppitz, J.</style></author><author><style face="normal" font="default" size="100%">T.M. Quinteiro</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path</style></title><secondary-title><style face="normal" font="default" size="100%">Semigroup Forum</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2021</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://link.springer.com/article/10.1007/s00233-021-10193-y</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">103</style></volume><pages><style face="normal" font="default" size="100%">87-105</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;/p&gt;
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