On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals

Authors

• HAYRULLAH AYIKFollow
• VÍTOR H. FERNANDESFollow
• EMRAH H. KORKMAZFollow

Author ORCID Identifier

HAYRULLAH AYIK: 0000-0001-7569-5597

VÍTOR FERNANDES: 0000-0003-1057-4975

EMRAH KORKMAZ: 0000-0002-4085-0419

Abstract

In this paper, we consider the monoid PIO_n of all partial order-preserving transformations on a chain with n elements whose domains and ranges are intervals, along with its submonoid PIO_n⁻ of order-decreasing transformations. Our main aim is to give presentations for PIO_n⁻ and PIO_n. Moreover, for both monoids, we describe regular elements and determine their ranks, cardinalities and the numbers of idempotents and nilpotents.

DOI

10.55730/1300-0098.3774

Keywords

Order-preserving, order-decreasing, partial transformations, rank, presentations

First Page

913

Last Page

932

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

AYIK, H, FERNANDES, V. H, & KORKMAZ, E. H (2026). On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals. Turkish Journal of Mathematics 50 (5): 913-932. https://doi.org/10.55730/1300-0098.3774