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arXiv · 1608.00243

A distribution on triples with maximum entropy marginal

Sergey Norin
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Abstract

We construct an $S_3$-symmetric probability distribution on $\{(a,b,c) \in \mathbb{Z}_{\geq 0}^3 \: : \: a+b+c =n \}$ such that its marginal achieves the maximum entropy among all probability distributions on $\{0,1,\ldots,n\}$ with mean $n/3$. Existence of such a distribution verifies a conjecture of Kleinberg, Sawin and Speyer, which is motivated by the study of sum-free sets.

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Sergey Norin. 2019-12-09. A distribution on triples with maximum entropy marginal. https://doi.org/10.1017/fms.2019.47

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