The dimension of suborders of the Boolean lattice

G. R. Brightwell, H. A. Kierstead, A. V. Kostochka, W. T. Trotter

Research output: Contribution to journalArticle

Abstract

We consider the order dimension of suborders of the Boolean lattice Bn. In particular we show that the suborder consisting of the middle two levels of Bn dimension at most of 6 log3n. More generally, we show that the suborder consisting of levels s and s+k of Bn has dimension O(k2 log n).

Original languageEnglish (US)
Pages (from-to)127-134
Number of pages8
JournalOrder
Volume11
Issue number2
DOIs
StatePublished - Jun 1 1994
Externally publishedYes

Keywords

  • Bollean lattice
  • Mathematics Subject Classifications (1991): 06A07, 05C35
  • Ordered set
  • dimension
  • suborder

ASJC Scopus subject areas

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

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  • Cite this

    Brightwell, G. R., Kierstead, H. A., Kostochka, A. V., & Trotter, W. T. (1994). The dimension of suborders of the Boolean lattice. Order, 11(2), 127-134. https://doi.org/10.1007/BF01108597