Theory of dimension for large discrete sets and applications

Details Theory of dimension for large discrete sets and applications Theory of dimension for large discrete sets and applications

2007-07-09

arxiv.org/abs/0707.1322v1

Mathematics

Combinatorics

27 pages

Scientific paper

We define two notions of discrete dimension based on the Minkowski and
Hausdorff dimensions in the continuous setting. After proving some basic
results illustrating these definitions, we apply this machinery to the study of
connections between the Erdos and Falconer distance problems in geometric
combinatorics and geometric measure theory, respectively.

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