On the monoid of order-preserving transformations of a finite chain whose ranges are intervals

Vítor H. Fernandes

doi:10.1007/s00233-024-10466-2

On the monoid of order-preserving transformations of a finite chain whose ranges are intervals

Vítor H. Fernandes

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

6 Citations (Scopus)

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Abstract

We give a presentation for the monoid IOn of all order-preserving transformations of an n-chain whose ranges are intervals. We also consider the submonoid IOn- of IOn consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.

Original language	English
Pages (from-to)	336–346
Number of pages	11
Journal	Semigroup Forum
Volume	109
Early online date	19 Aug 2024
DOIs	https://doi.org/10.1007/s00233-024-10466-2
Publication status	Published - Oct 2024

Keywords

Order-decreasing
Order-preserving
Presentations
Transformations

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10.1007/s00233-024-10466-2Licence: CC BY

On the monoid of order-preserving transformations of aFinal published version, 224 KBLicence: CC BY

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title = "On the monoid of order-preserving transformations of a finite chain whose ranges are intervals",

abstract = "We give a presentation for the monoid IOn of all order-preserving transformations of an n-chain whose ranges are intervals. We also consider the submonoid IOn- of IOn consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.",

keywords = "Order-decreasing, Order-preserving, Presentations, Transformations",

author = "Fernandes, \{V{\'i}tor H.\}",

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year = "2024",

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doi = "10.1007/s00233-024-10466-2",

language = "English",

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AU - Fernandes, Vítor H.

N1 - Funding Information: This work is funded by national funds through the FCT \u2013 Funda\u00E7\u00E3o para a Ci\u00EAncia e a Tecnologia, I.P., under the scope of the (Center for Mathematics and Applications) projects UIDB/00297/2020 ( https://doi.org/10.54499/UIDB/00297/2020 ) and UIDP/00297/2020 ( https://doi.org/10.54499/UIDP/00297/2020 ). Publisher Copyright: © The Author(s) 2024.

PY - 2024/10

Y1 - 2024/10

N2 - We give a presentation for the monoid IOn of all order-preserving transformations of an n-chain whose ranges are intervals. We also consider the submonoid IOn- of IOn consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.

AB - We give a presentation for the monoid IOn of all order-preserving transformations of an n-chain whose ranges are intervals. We also consider the submonoid IOn- of IOn consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.

KW - Order-decreasing

KW - Order-preserving

KW - Presentations

KW - Transformations

UR - https://www.scopus.com/pages/publications/85201550668

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DO - 10.1007/s00233-024-10466-2

M3 - Article

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VL - 109

SP - 336

EP - 346

JO - Semigroup Forum

JF - Semigroup Forum

ER -

On the monoid of order-preserving transformations of a finite chain whose ranges are intervals

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