[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2014.51.4.1055

GENERATING SETS OF STRICTLY ORDER-PRESERVING TRANSFORMATION SEMIGROUPS ON A FINITE SET

Ayik, Hayrullah (Department of Mathematics Cukurova University)
Bugay, Leyla (Department of Mathematics Cukurova University)

Publication Information

Bulletin of the Korean Mathematical Society / v.51, no.4, 2014 , pp. 1055-1062 More about this Journal

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 semi-group; idempotents; (minimal) generating set; rank;

Citations & Related Records

Reference

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