On the rank of monoids of endomorphisms of a finite directed path

Vítor H. Fernandes; Tânia Paulista

doi:10.1142/S1793557123500699

On the rank of monoids of endomorphisms of a finite directed path

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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 wEndP→n of all weak endomorphisms of a directed path with n vertices, which is a submonoid of the widely studied monoid n of all order-preserving transformations of an n-chain. Also, we describe the regular elements of wEndP→n and calculate its size and number of idempotents.

Original language	English
Article number	2350069
Number of pages	10
Journal	Asian-European Journal of Mathematics
Volume	16
Issue number	4
Early online date	2022
DOIs	https://doi.org/10.1142/S1793557123500699
Publication status	Published - 2023

Keywords

generators
Graph endomorphisms
paths
rank

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10.1142/S1793557123500699

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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 wEndP→n of all weak endomorphisms of a directed path with n vertices, which is a submonoid of the widely studied monoid n of all order-preserving transformations of an n-chain. Also, we describe the regular elements of wEndP→n and calculate its size and number of idempotents.",

keywords = "generators, Graph endomorphisms, paths, rank",

author = "Fernandes, {V{\'i}tor H.} and T{\^a}nia Paulista",

note = "Publisher Copyright: {\textcopyright} 2023 World Scientific Publishing Company. This work is funded by national funds through the FCT -Fundacao para a Ciencia e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). The authors would like to thank the anonymous referee for the valuable comments that allowed us to improve the proof of Lemma 3.2.",

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T1 - On the rank of monoids of endomorphisms of a finite directed path

AU - Fernandes, Vítor H.

AU - Paulista, Tânia

N1 - Publisher Copyright: © 2023 World Scientific Publishing Company. This work is funded by national funds through the FCT -Fundacao para a Ciencia e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). The authors would like to thank the anonymous referee for the valuable comments that allowed us to improve the proof of Lemma 3.2.

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N2 - 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 wEndP→n of all weak endomorphisms of a directed path with n vertices, which is a submonoid of the widely studied monoid n of all order-preserving transformations of an n-chain. Also, we describe the regular elements of wEndP→n and calculate its size and number of idempotents.

AB - 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 wEndP→n of all weak endomorphisms of a directed path with n vertices, which is a submonoid of the widely studied monoid n of all order-preserving transformations of an n-chain. Also, we describe the regular elements of wEndP→n and calculate its size and number of idempotents.

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KW - paths

KW - rank

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JO - Asian-European Journal of Mathematics

JF - Asian-European Journal of Mathematics

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On the rank of monoids of endomorphisms of a finite directed path

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