On exponential Freiman dimension

2025/12/16 by Lim, Jeck, Mudgal, Akshat, Pohoata, Cosmin +1
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2512.14403

Abstract

The exponential Freiman dimension of a finite set A ⊂ ℝ^m, introduced by Green and Tao in 2006, represents the largest positive integer d for which A contains the vertices of a non-degenerate d-dimensional parallelepiped. For every d ≥ 1, we precisely determine the largest constant C_d>0 (exponential in d) for which |A+A| ≥ C_d|A| - O_d(1) holds for all sets A with exponential Freiman dimension d.

Citations

• On a conjecture of Marton
• Compressions, convex geometry and the Freiman-Bilu theorem
• Permutohedra, associahedra, and beyond

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