Generating sets of certain finite subsemigroups of monotone partial bijections

Authors : Leyla BUGAY, HAYRULLAH AYIK

Pages : 2270-2278

View : 14 | Download : 6

Publication Date : 0000-00-00

Article Type : Research Paper

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 insert ignore into journalissuearticles values(minimal); generating sets of the subsemigroups $PODI_{n,r}=\{ \alpha \in PODI_{n}:|\iminsert ignore into journalissuearticles values(\alpha);|\leq r\}$, $POI_{n,r}=\{ \alpha \in POI_{n}: |\iminsert ignore into journalissuearticles values(\alpha);|\leq r\}$, 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 $0\leq r\leq n-1$.
Keywords : Partial bijection, isotone antitone monotone map minimal, generating set