Theory of dimension for large discrete sets and applications

2007/07/09 by Alex Iosevich, Iosevich, Alex, Misha Rudnev +3
Mathematics · #52C10 #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #math.CA #math.CO #msc:52C10

paper · pdf · doi:10.48550/arxiv.0707.1322

27 pages

arxiv created 2007/07/09 · arxiv updated 2009/12/01

Abstract

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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