A note on the colorful fractional Helly theorem
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colorfulfractionalhellytheoremversionresultclassicalcombined
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Helly's theorem is a classical result concerning the intersection patterns of convex sets in $\mathbb{R}^d$. Two important generalizations are the colorful version and the fractional version. Recently, B\'{a}r\'{a}ny et al. combined the two, obtaining a colorful fractional Helly theorem. In this paper, we give an improved version of their result.
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Cited by 1 Pith paper
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Fractional Helly property and combinatorics of forking in NTP$_2$ theories
Defines FHP theories via the Fractional Helly Property as a new subclass of low NTP2 theories, provides algebraic examples, and derives partial results on forking combinatorics and two-cardinal counting functions.
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