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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Bibliographic Details
Date:2025
Main Authors: Ayık, Hayrullah, Fernandes, Vítor H., Korkmaz, Emrah
Format: Article
Language:English
Published: 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
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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 \(\mathcal{PIM}_{n}\).