Shatter Functions with Polynomial Growth Rates

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2019Embargo end date: 01 Jan 2017 France English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Discrete Mathematics, volume 33, pages 784-794 (issn: 0895-4801, eissn: 1095-7146,

Copyright policy )Funded by:NSF | Geometry in combinatorics, NSF | CAREER: Algebraic extrema...

Authors: Boris Bukh; Xavier Goaoc;

doi: 10.1137/17m1113680 , 10.48550/arxiv.1701.06632

arXiv: 1701.06632

Shatter Functions with Polynomial Growth Rates

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Abstract

We study how a single value of the shatter function of a set system restricts its asymptotic growth. Along the way, we refute a conjecture of Bondy and Hajnal which generalizes Sauer's Lemma.

9 pages, 3 figures

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France

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Keywords

FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Sauer's lemma, Extremal set theory, Discrete geometry, 05D05, 52C99, [MATH] Mathematics [math], [INFO] Computer Science [cs], extremal set theory, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), shatter function, Computer Science - Discrete Mathematics

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