Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3341
Abstract
In the present paper, we consider the semigroup $O_{n,p}$ of all order-preserving full transformations $\alpha $ on an n-elements chain $X_{n}$% , where $p\in X_{n}$ is the only fixed point of $\alpha $. The nilpotent semigroup $O_{n,p}$ was first studied by Ayik et al. in 2011. Moreover, $% O_{n,1}$ is the maximal nilpotent subsemigroup of the Catalan Monoid $C_{n}$. Its rank is the difference of the $(n-1)$th and the $(n-2)$th Catalan number. The aim of the present paper is to provide further fundamental information about the nilpotent semigroup $O_{n,p}$. We will calculate the rank of $O_{n,p}$ for $% p>1$ and provide a semigroup presentation for $O_{n,1}$.
Keywords
Order-preserving transformations, fixed point transformations, presentations, ranks
First Page
3408
Last Page
3418
Recommended Citation
KOPPITZ, JOERG and WORAWISET, SOMNUEK
(2022)
"Ranks and presentations for order-preserving transformations with one fixed point,"
Turkish Journal of Mathematics: Vol. 46:
No.
8, Article 23.
https://doi.org/10.55730/1300-0098.3341
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss8/23
