March 3, 2026Open Access

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

Key Points

Cardinalities and ranks of the monoid PIMn are determined, revealing its structural complexity.
The number of nilpotent elements in PIMn is quantified, providing insights into its properties.
Relations between PIMn and its submonoid IMn are established, aiding in understanding transformations.
Presentations for both monoids are defined, enhancing clarity in their algebraic structure.

Abstract

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

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Discussion

Cite this study

Ayik et al. (Wed,) studied this question.

www.synapsesocial.com/papers/69a7622dc6e9836116a3062b

Authors

Hayrullah Ayik

Vitor H. Fernandes

Emrah Korkmaz

Actions

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

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

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Cite this study

Authors

Actions

References and Citations

Citation Network

Connected Papers

Discussion