The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence
- A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.
| Author details: | Vitor H. Fernandes, Jörg KoppitzORCiDGND, Tiwadee MusunthiaGND |
|---|---|
| DOI: | https://doi.org/10.1007/s40840-017-0598-1 |
| ISSN: | 0126-6705 |
| ISSN: | 2180-4206 |
| Title of parent work (English): | Bulletin of the Malaysian Mathematical Sciences Society volume |
| Publisher: | Malaysian mathematical sciences sciences soc |
| Place of publishing: | Pulau Punang |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2019/01/31 |
| Publication year: | 2019 |
| Release date: | 2020/11/18 |
| Tag: | Fence; Idempotents; Order-preserving; Rank of semigroup; Transformation semigroups; Zig-zag order |
| Volume: | 42 |
| Issue: | 5 |
| Number of pages: | 21 |
| First page: | 2191 |
| Last Page: | 2211 |
| Funding institution: | CMA [UID/MAT/00297/2013]; Research Fund of Faculty of Science, Silpakorn University [SRF-PRG-2557-02] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
