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


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AYIK H. , BUGAY L.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.51, no.4, pp.1055-1062, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 4
  • Publication Date: 2014
  • Doi Number: 10.4134/bkms.2014.51.4.1055
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.1055-1062

Abstract

Let O-n and POn, denote the order-preserving transformation and the partial order-preserving transformation semigroups on the set X-n = {1,...,n}, respectively. Then the strictly partial order-preserving transformation semigroup SPOn on the set X-n, under its natural or der, is defined by SPOn = POn\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 <= r <= n - 1.