The Erdős distinct subset sums problem in a modular setting

2023/08/07 by Cambie, Stijn, Gao, Jun, Kim, Younjin +1
#11B13 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2308.03748

Abstract

We prove the following variant of the Erdős distinct subset sums problem. Given t ≥ 0 and sufficiently large n, every n-element set A whose subset sums are distinct modulo N=2ⁿ+t satisfies max A ≥ ((1)/(3)-o(1))N. Furthermore, we provide examples showing that the constant \frac 13 is best possible. For small values of t, we characterise the structure of all sumset-distinct sets modulo N=2ⁿ+t of cardinality n.

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