A DISTRIBUTION ON TRIPLES WITH MAXIMUM ENTROPY MARGINAL
Keyword(s):
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.
2021 ◽
Vol 118
(40)
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pp. e2025782118
2020 ◽
2018 ◽
Vol 107
(3)
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pp. 302-318
1984 ◽
Vol R-33
(4)
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pp. 353-357
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2008 ◽
Vol 16
(05)
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pp. 699-713
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Keyword(s):
2011 ◽
Vol 09
(supp01)
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pp. 39-47