Generating the full transformation semigroup using order preserving mappings

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

For a linearly ordered set X we consider the relative rank of the semigroup of all order preserving mappings O-X on X modulo the full transformation semigroup Ex. In other words, we ask what is the smallest cardinality of a set A of mappings such that <O-X boolean OR A> = T-X. When X is countably infinite or well-ordered (of arbitrary cardinality) we show that this number is one, while when X = R (the set of real numbers) it is uncountable.

Original languageEnglish
Pages (from-to)557-566
Number of pages10
JournalGlasgow Mathematical Journal
Volume45
Issue number3
DOIs
Publication statusPublished - Sept 2003

Keywords

  • Ranks

Fingerprint

Dive into the research topics of 'Generating the full transformation semigroup using order preserving mappings'. Together they form a unique fingerprint.

Cite this