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arXiv · 2112.13427

On the Rank of Monoids of Endomorphisms of a Finite Directed Path

Vítor Hugo Fernandes·Tânia Paulista
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Abstract

In this paper we consider endomorphisms of a finite directed path from monoid generators perspective. Our main aim is to determine the rank of the monoid $\wEnd\vec{P}_n$ of all weak endomorphisms of a directed path with $n$ vertices, which is a submonoid of the widely studied monoid $\On$ of all order-preserving transformations of a $n$-chain. Also, we describe the regular elements of $\wEnd\vec{P}_n$ and calculate its size and number of idempotents.

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BibTeXRIS

Vítor Hugo Fernandes, Tânia Paulista. 2021-12-26. On the Rank of Monoids of Endomorphisms of a Finite Directed Path. https://arxiv.org/abs/2112.13427

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