Ranks and presentations of some normally ordered inverse semigroups

Rita Caneco; Vítor H. Fernandes; Teresa M. Quinteiro

doi:10.1007/s10998-022-00448-8

Ranks and presentations of some normally ordered inverse semigroups

Rita Caneco, Vítor H. Fernandes, Teresa M. Quinteiro

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper we compute the rank and exhibit a presentation for the monoids of all P-stable and P-order preserving partial permutations on a finite set Ω , with P an ordered uniform partition of Ω. These (inverse) semigroups constitute a natural class of generators of the pseudovariety of inverse semigroups NO of all normally ordered (finite) inverse semigroups.

Original language	English
Pages (from-to)	435-447
Number of pages	13
Journal	Periodica Mathematica Hungarica
Volume	85
Issue number	2
DOIs	https://doi.org/10.1007/s10998-022-00448-8
Publication status	Published - Dec 2022

Keywords

Normally ordered inverse semigroups
Presentations
Ranks
Transformations

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10.1007/s10998-022-00448-8

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title = "Ranks and presentations of some normally ordered inverse semigroups",

abstract = "In this paper we compute the rank and exhibit a presentation for the monoids of all P-stable and P-order preserving partial permutations on a finite set Ω , with P an ordered uniform partition of Ω. These (inverse) semigroups constitute a natural class of generators of the pseudovariety of inverse semigroups NO of all normally ordered (finite) inverse semigroups.",

keywords = "Normally ordered inverse semigroups, Presentations, Ranks, Transformations",

author = "Rita Caneco and Fernandes, \{V{\'i}tor H.\} and Quinteiro, \{Teresa M.\}",

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doi = "10.1007/s10998-022-00448-8",

language = "English",

volume = "85",

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journal = "Periodica Mathematica Hungarica",

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AU - Fernandes, Vítor H.

AU - Quinteiro, Teresa M.

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Y1 - 2022/12

N2 - In this paper we compute the rank and exhibit a presentation for the monoids of all P-stable and P-order preserving partial permutations on a finite set Ω , with P an ordered uniform partition of Ω. These (inverse) semigroups constitute a natural class of generators of the pseudovariety of inverse semigroups NO of all normally ordered (finite) inverse semigroups.

AB - In this paper we compute the rank and exhibit a presentation for the monoids of all P-stable and P-order preserving partial permutations on a finite set Ω , with P an ordered uniform partition of Ω. These (inverse) semigroups constitute a natural class of generators of the pseudovariety of inverse semigroups NO of all normally ordered (finite) inverse semigroups.

KW - Normally ordered inverse semigroups

KW - Presentations

KW - Ranks

KW - Transformations

UR - https://www.scopus.com/pages/publications/85126442330

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DO - 10.1007/s10998-022-00448-8

M3 - Article

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VL - 85

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EP - 447

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

IS - 2

ER -

Ranks and presentations of some normally ordered inverse semigroups

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Keywords

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