On monoids of monotone partial transformations of a finite chain whose domains and ranges are intervals
In this note, we consider the monoid \(\mathcal{PIM}_{n}\) of all partial monotone transformations on a chain with \(n\) elements whose domains and ranges are intervals and its submonoid \(\mathcal{IM}_{n}\) constituted by the full transformations. For both of these monoids, our aim is to determine...
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| Date: | 2025 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2025
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2403 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543302121160704 |
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| author | Ayık, Hayrullah Fernandes, Vítor H. Korkmaz, Emrah |
| author_facet | Ayık, Hayrullah Fernandes, Vítor H. Korkmaz, Emrah |
| author_sort | Ayık, Hayrullah |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2025-10-27T20:24:52Z |
| description | In this note, we consider the monoid \(\mathcal{PIM}_{n}\) of all partial monotone transformations on a chain with \(n\) elements whose domains and ranges are intervals and its submonoid \(\mathcal{IM}_{n}\) constituted by the full transformations. For both of these monoids, our aim is to determine their cardinalities and ranks and define them by means of presentations. We also calculate the number of nilpotent elements of \(\mathcal{PIM}_{n}\). |
| first_indexed | 2025-12-02T15:26:22Z |
| format | Article |
| id | admjournalluguniveduua-article-2403 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:26:22Z |
| publishDate | 2025 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-24032025-10-27T20:24:52Z On monoids of monotone partial transformations of a finite chain whose domains and ranges are intervals Ayık, Hayrullah Fernandes, Vítor H. Korkmaz, Emrah transformations, monotone, rank, presentations 20M20, 20M05, 20M10 In this note, we consider the monoid \(\mathcal{PIM}_{n}\) of all partial monotone transformations on a chain with \(n\) elements whose domains and ranges are intervals and its submonoid \(\mathcal{IM}_{n}\) constituted by the full transformations. For both of these monoids, our aim is to determine their cardinalities and ranks and define them by means of presentations. We also calculate the number of nilpotent elements of \(\mathcal{PIM}_{n}\). Lugansk National Taras Shevchenko University 2025-10-27 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2403 10.12958/adm2403 Algebra and Discrete Mathematics; Vol 40, No 1 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2403/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2403/1310 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2403/1326 Copyright (c) 2025 Algebra and Discrete Mathematics |
| spellingShingle | transformations monotone rank presentations 20M20 20M05 20M10 Ayık, Hayrullah Fernandes, Vítor H. Korkmaz, Emrah On monoids of monotone partial transformations of a finite chain whose domains and ranges are intervals |
| title | On monoids of monotone partial transformations of a finite chain whose domains and ranges are intervals |
| title_full | On monoids of monotone partial transformations of a finite chain whose domains and ranges are intervals |
| title_fullStr | On monoids of monotone partial transformations of a finite chain whose domains and ranges are intervals |
| title_full_unstemmed | On monoids of monotone partial transformations of a finite chain whose domains and ranges are intervals |
| title_short | On monoids of monotone partial transformations of a finite chain whose domains and ranges are intervals |
| title_sort | on monoids of monotone partial transformations of a finite chain whose domains and ranges are intervals |
| topic | transformations monotone rank presentations 20M20 20M05 20M10 |
| topic_facet | transformations monotone rank presentations 20M20 20M05 20M10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2403 |
| work_keys_str_mv | AT ayıkhayrullah onmonoidsofmonotonepartialtransformationsofafinitechainwhosedomainsandrangesareintervals AT fernandesvitorh onmonoidsofmonotonepartialtransformationsofafinitechainwhosedomainsandrangesareintervals AT korkmazemrah onmonoidsofmonotonepartialtransformationsofafinitechainwhosedomainsandrangesareintervals |