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An arithmetic regularity lemma, associated counting lemma, and applications

Abstract:

Szemeredi's regularity lemma can be viewed as a rough structure theorem for arbitrary dense graphs, decomposing such graphs into a structured piece (a partition into cells with edge densities), a small error (corresponding to irregular cells), and a uniform piece (the pseudorandom deviations from the edge densities). We establish an arithmetic regularity lemma that similarly decomposes bounded functions f : [N] -> C, into a (well-equidistributed, virtual) -step nilsequence, an error which ...

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Publication date:
2010-02-10
URN:
uuid:c0cd0ea1-877d-4f6e-bcb0-90376aa96d82
Source identifiers:
398469
Local pid:
pubs:398469

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