Generating sets of strictly order-preserving transformation semigroups on a finite set
Bull. Korean Math. Soc. 2014 Vol. 51, No. 4, 1055-1062
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
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