H. Pham

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20242026

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4 papers · 1 filter

math.CO2026

On Graham's rearrangement conjecture

Huy Tuan Pham, Lisa Sauermann

Graham conjectured in 1971 that for any prime $p$ , any subset $S \subseteq Z_{p} ∖ {0}$ admits an ordering $s_{1}, s_{2}, \dots, s_{∣ S ∣}$ where all partial sums $s_1, s_1+s…

math.CO2025

Sunflowers in set systems with small VC-dimension

JÃ³zsef Balogh, Anton Bernshteyn, Michelle Delcourt +2

A family of $r$ distinct sets ${A_{1}, \dots, A_{r}}$ is an $r$ -sunflower if for all $1 ⩽ i < j ⩽ r$ and $1 ⩽ i^{'} < j^{'} ⩽ r$ , we have $A_i \cap A_j = A_…

math.CO2025

Sharp bound for the ErdÅs-Straus non-averaging set problem

Huy Tuan Pham, Dmitrii Zakharov

A set of integers $A$ is non-averaging if there is no element $a$ in $A$ which can be written as an average of a subset of $A$ not containing $a$ . We show that the largest non-aver…

math.CO2024

An explicit economical additive basis

Vishesh Jain, Huy Tuan Pham, Mehtaab Sawhney +1

We present an explicit subset $A \subseteq N = {0, 1, \dots}$ such that $A + A = N$ and for all $ε > 0$ , \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2):…

On Graham's rearrangement conjecture

Sunflowers in set systems with small VC-dimension

Sharp bound for the ErdÅs-Straus non-averaging set problem

An explicit economical additive basis

Sharp bound for the ErdÅs-Straus non-averaging set problem