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 log2 d. We conjecture f(d)=θ(d 2), and prove something close to this for height-3 lattices, but in general we do not even know whether f(d)/d→∞.
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Communicated by I. Rival
Supported in part by NSF grant MCS 83-01867, AFORS grant number 0271 and a Sloan Research Fellowship.
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Füredi, Z., Kahn, J. Dimension versus size. Order 5, 17–20 (1988). https://doi.org/10.1007/BF00143893
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DOI: https://doi.org/10.1007/BF00143893