Representing an ordered set as the intersection of super greedy linear extensions

H. A. Kierstead, W. T. Trotter, B. Zhou

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

A linear extension [x1<x2<...<xt] of a finite ordered set P=(P, <) is super greedy if it can be obtained using the following procedure: Choose x1 to be a minimal element of P; suppose x1,..., xi have been chosen; define p(x) to be the largest j≤i such that xj<x if such a j exists and 0 otherwise; choose xi+1 to be a minimal element of P-{x1,..., xi} which maximizes p. Every finite ordered set P can be represented as the intersection of a family of super greedy linear extensions, called a super greedy realizer of P. The super greedy dimension of P is the minimum cardinality of a super greedy realizer of P. Best possible upper bounds for the super greedy dimension of P are derived in terms of |P-A| and width (P-A), where A is a maximal antichain.

Original languageEnglish (US)
Pages (from-to)293-311
Number of pages19
JournalOrder
Volume4
Issue number3
DOIs
StatePublished - Sep 1 1987
Externally publishedYes

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Keywords

  • AMS subject classifications (1980): 06A05
  • Ordered sets
  • linear extensions
  • super greedy dimensions

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Theory and Mathematics

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