Degrees of freedom versus dimension for containment orders

Noga Alon, Edward R. Scheinerman

Research output: Contribution to journalArticle

29 Scopus citations

Abstract

Given a family of sets L, where the sets in L admit k 'degrees of freedom', we prove that not all (k+1)-dimensional posets are containment posets of sets in L. Our results depend on the following enumerative result of independent interest: Let P(n, k) denote the number of partially ordered sets on n labeled elements of dimension k. We show that log P(n, k)∼nk log n where k is fixed and n is large.

Original languageEnglish (US)
Pages (from-to)11-16
Number of pages6
JournalOrder
Volume5
Issue number1
DOIs
StatePublished - Mar 1 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

Keywords

  • AMS subject classifications (1980): 06A10 (primary), 14N10 (secondary)
  • Partially ordered set
  • containment order
  • degrees of freedom
  • partial order dimension

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