A distribution on triples with maximum entropy marginal

Abstract

We construct an $S_3$-symmetric probability distribution on $\{(a,b,c)\in {\mathbb{Z}}_{\ge 0}^3:a+b+c=n\}$ such that its marginal achieves the maximum entropy among all probability distributions on $\{0,1,\dots ,n\}$ 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.

corrected an error in the estimates used in the proof of the main result

References in corpus (4)

• Progression-free sets in Z_4^n are exponentially small
• On cap sets and the group-theoretic approach to matrix multiplication
• The Growth Rate of Tri-Colored Sum-Free Sets
• On large subsets of $F_q^n$ with no three-term arithmetic progression

Cited by in corpus (5)

• On cap sets and the group-theoretic approach to matrix multiplication
• The Growth Rate of Tri-Colored Sum-Free Sets
• A lower bound for the $k$-multicolored sum-free problem in ${\mathbb{Z}}_m^n$
• Universal points in the asymptotic spectrum of tensors
• Removal lemmas and approximate homomorphisms