Generating sets of strictly order-preserving transformation semigroups on a finite set
Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 1055-1062
https://doi.org/10.4134/BKMS.2014.51.4.1055
Published online July 1, 2014
Hayrullah Ayik and Leyla Bugay
\c{C}ukurova University, \c{C}ukurova University
Abstract : Let $O_{n}$ and $PO_{n}$ denote the order-preserving transformation and the partial order-preserving transformation semigroups on the set $X_{n}=\{1,\ldots ,n\}$, respectively. Then the strictly partial order-preserving transformation semigroup $SPO_{n}$ on the set $X_{n}$, under its natural order, is defined by $SPO_{n} = PO_{n} \setminus O_{n}$. In this paper we find necessary and sufficient conditions for any subset of $SPO(n,r)$ to be a (minimal) generating set of $SPO(n,r)$ for $2\leq r\leq n-1$.
Keywords : (partial/strictly partial) order-preserving transformation semigroup, idempotents, (minimal) generating set, rank
MSC numbers : 20M20
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd