Dimension versus size

Zoltán Füredi, Jeff Kahn

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We investigate the behavior of f(d), the least size of a lattice of order dimension d. In particular we show that the lattice of a projective plane of order n has dimension at least n/ln(n), so that f(d)=O(d)2 log2d. We conjecture f(d)=θ(d2), and prove something close to this for height-3 lattices, but in general we do not even know whether f(d)/d→∞.

Original languageEnglish
Pages (from-to)17-20
Number of pages4
JournalOrder
Volume5
Issue number1
DOIs
Publication statusPublished - Mar 1988

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Order Dimension
Projective plane

Keywords

  • AMS subject classifications (1980): 06A10, 06A23
  • Lattice
  • least size
  • order dimension

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Dimension versus size. / Füredi, Zoltán; Kahn, Jeff.

In: Order, Vol. 5, No. 1, 03.1988, p. 17-20.

Research output: Contribution to journalArticle

Füredi, Z & Kahn, J 1988, 'Dimension versus size', Order, vol. 5, no. 1, pp. 17-20. https://doi.org/10.1007/BF00143893
Füredi, Zoltán ; Kahn, Jeff. / Dimension versus size. In: Order. 1988 ; Vol. 5, No. 1. pp. 17-20.
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