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, L, & AYIK, H (2018). Generating sets of certain finite subsemigroups of monotone partial bijections. Turkish Journal of Mathematics 42 (5): 2270-2278. https://doi.org/10.3906/mat-1710-86
