On the monoid of partial order-preserving transformations of a finite chain whose domains and ranges are intervals
- 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." (Submitted).
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.
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