Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path

Citation:
Dimitrova, I., V. H. Fernandes, J. Koppitz, and T. M. Quinteiro. "Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path." Semigroup Forum. 103 (2021): 87-105.

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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