Generating sets of certain finite subsemigroups of monotone partial bijections
| Autor: | Hayrullah Ayik, Leyla Bugay |
|---|---|
| Přispěvatelé: | Çukurova Üniversitesi |
| Rok vydání: | 2018 |
| Předmět: |
Combinatorics
Mathematics::Combinatorics Monotone polygon Mathematics::Commutative Algebra Partial bijection isotone/antitone/monotone map (minimal) generating set General Mathematics Isotone/antitone/monotone map Partial bijection (minimal) generating set Bijection injection and surjection Mathematics |
| Zdroj: | Volume: 42, Issue: 5 2270-2278 Turkish Journal of Mathematics |
| ISSN: | 1303-6149 1300-0098 |
| DOI: | 10.3906/mat-1710-86 |
| Popis: | 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 $0\leq r\leq n-1$. |
| Databáze: | OpenAIRE |
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