On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals (DOI 10.55730/1300-0098.3774)

Citation:
Ayık, H., Vítor H. Fernandes, and E. Korkmaz. "On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals (DOI 10.55730/1300-0098.3774)." Turkish Journal of Mathematics. 50.5 (2026): 913-932.

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.

Related External Link

arXiv:

https://arxiv.org/pdf/2503.19459