On monoids of monotone partial transformations of a finite chain whose domains and ranges are intervals

2025/04/28 by Hayrullah Ayık, Vítor H. Fernandes, Ayık, Hayrullah +3
Computer Science · Mathematics · #20M05 #20M10 #20M20 #Advanced Algebra and Logic #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2504.19618

openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we consider the monoid PIM_n of all partial monotone transformations on a chain with n elements whose domains and ranges are intervals and its submonoid 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 PIM_n.

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