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arXiv · 1702.03956

Thicket Density

Siddharth Bhaskar
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Abstract

We define a new type of "shatter function" for set systems that satisfies a Sauer-Shelah type dichotomy, but whose polynomial-growth case is governed by Shelah's 2-rank instead of VC dimension. We identify the rate of growth of this shatter function, the quantity analogous to VC density, with Shelah's $\omega$-rank.

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Siddharth Bhaskar. 2017-02-13. Thicket Density. https://doi.org/10.1017/jsl.2020.55

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