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Journal Articles SIAM Journal on Discrete Mathematics Year : 2019

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.

Dates and versions

hal-02050524 , version 1 (27-02-2019)

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Boris Bukh, Xavier Goaoc. Shatter functions with polynomial growth rates. SIAM Journal on Discrete Mathematics, 2019, 33 (2), pp.784-794. ⟨10.1137/17M1113680⟩. ⟨hal-02050524⟩
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