Turkish Journal of Mathematics
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 $0\leq r\leq n-1$.
DOI
10.3906/mat-1710-86
Keywords
Partial bijection, isotone/antitone/monotone map, (minimal) generating set
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
