Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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GENERATING SETS OF STRICTLY ORDER-PRESERVING TRANSFORMATION SEMIGROUPS ON A FINITE SET

  • Received : 2013.08.14
  • Published : 2014.07.31
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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 $2{\leq}r{\leq}n-1$.

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References

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