On the number of discrete chains in the plane

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• Nóra Frankl (LSE)
• Thursday 07 November 2019, 14:00-15:00
• Watson LTB.

If you have a question about this talk, please contact Eoin Long.

Determining the maximum number of unit distances that can be spanned by n points in the plane is a difficult problem, which is wide open. The following more general question was recently considered by Eyvindur Ari Palsson, Steven Senger, and Adam Sheffer. For given distances t_1,...,t_k a (k+1)-tuple (p_1,...,p_{k+1}) is called a k-chain if ||x_i-x_{i+1}||=t_i for i=1,...,k. What is the maximum possible number of k-chains that can be spanned by a set of n points in the plane? Improving the result of Palsson, Senger and Sheffer, we determine this maximum up to a polylogarithmic factor (which, for k=1 mod 3 involves the maximum number of unit distances). We also consider some generalisations, and the analogous question in R^3. Joint work with Andrey Kupvaskii.

This talk is part of the Combinatorics and Probability seminar series.

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• Combinatorics and Probability seminar
• School of Mathematics events
• Watson LTB

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