Geodesic
A DISTRIBUTION ON TRIPLES WITH MAXIMUM ENTROPY MARGINAL
Forum of Mathematics, Sigma, Tome 7 (2019)

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We construct an $S_{3}$-symmetric probability distribution on $\{(a,b,c)\in \mathbb{Z}_{{\geqslant}0}^{3}\,:\,a+b+c=n\}$ 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 et al. [‘The growth rate of tri-colored sum-free sets’, Discrete Anal. (2018), Paper No. 12, arXiv:1607.00047v1], which is motivated by the study of sum-free sets. 
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     author = {SERGEY NORIN},
     title = {A {DISTRIBUTION} {ON} {TRIPLES} {WITH} {MAXIMUM} {ENTROPY} {MARGINAL}},
     journal = {Forum of Mathematics, Sigma},
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SERGEY NORIN. A DISTRIBUTION ON TRIPLES WITH MAXIMUM ENTROPY MARGINAL. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.47

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