Ranks of monoids of endomorphisms of a finite undirected path

Abstract

In this paper we study the widely considered endomorphisms and weak endomorphisms of a finite undirected path from monoid generators perspective. Our main aim is to determine the ranks of the monoids $wEnd{P}_n$ and $End{P}_n$ of all weak endomorphisms and all endomorphisms of the undirected path $P_n$ with $n$ vertices. We also consider strong and strong weak endomorphisms of $P_n$.

Cited by in corpus (2)

• Minimal generating sets for matrix monoids
• Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path