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 |
| Published: |
Lugansk National Taras Shevchenko University
2025
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| Subjects: | |
| 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| Summary: | 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 \(\mathcal{PIM}_{n}\). |
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