GENERATING SETS OF STRICTLY ORDER-PRESERVING TRANSFORMATION SEMIGROUPS ON A FINITE SET
Hayrullah Ayık, Leyla BUGAY · Bulletin of the Korean Mathematical Society · 2014
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 $2{\leq}r{\leq}n-1$ .