Turkish Journal of Mathematics
DOI
10.3906/mat-1710-86
Abstract
Let $I_{n}$ be the symmetric inverse semigroup, and let $PODI_{n}$ and $POI_{n}$ be its subsemigroups of monotone partial bijections and of isotone partial bijections on $X_{n}=\{1,\ldots ,n\}$ under its natural order, respectively. In this paper we characterize the structure of (minimal) generating sets of the subsemigroups $PODI_{n,r}=\{ \alpha \in PODI_{n}: \im(\alpha) \leq r\}$, $POI_{n,r}=\{ \alpha \in POI_{n}: \im(\alpha) \leq r\}$, and $E_{n,r}=\{ \id_{A}\in I_{n}:A\subseteq X_n\mbox{ and } A \leq r\}$ where $id_{A}$ is the identity map on $A\subseteq X_n$ for $0\leq r\leq n-1$.
First Page
2270
Last Page
2278
Recommended Citation
BUGAY, LEYLA and AYIK, HAYRULLAH
(2018)
"Generating sets of certain finite subsemigroups of monotone partial bijections,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 13.
https://doi.org/10.3906/mat-1710-86
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/13
