Dimension versus size

Zoltán Füredi, Jeff Kahn

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 (US)
Pages (from-to)17-20
Number of pages4
Issue number1
StatePublished - Mar 1988

All Science Journal Classification (ASJC) codes

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


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


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