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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Datum:2025
Hauptverfasser: Ayık, Hayrullah, Fernandes, Vítor H., Korkmaz, Emrah
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2025
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Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2403
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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Zusammenfassung: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 \(\mathcal{PIM}_{n}\).