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- W4310403839 abstract "A family $mathcal{F}subset 2^G$ of subsets of an abelian group $G$ is a Sidon system if the sumsets $A+B$ with $A,Bin mathcal{F}$ are pairwise distinct. Cilleruelo, Serra and the author previously proved that the maximum size $F_k(n)$ of a Sidon system consisting of $k$-subsets of the first $n$ positive integers satisfies $C_k n^{k-1}leq F_k(n) leq binom{n-1}{k-1}+n-k$ for some constant $C_k$ only depending on $k$. We close the gap by proving an essentially tight structural result that in particular implies $F_k(n)geq (1-o(1))binom{n}{k-1}$. We also use this to establish a result about the size of the largest Sidon system in the binomial random family $binom{[n]}{k}_p$. Extensions to $h$-fold sumsets for any fixed $hgeq 3$ are also obtained." @default.
- W4310403839 created "2022-12-10" @default.
- W4310403839 creator A5048407815 @default.
- W4310403839 date "2022-11-25" @default.
- W4310403839 modified "2023-09-27" @default.
- W4310403839 title "The structure of Sidon set systems" @default.
- W4310403839 doi "https://doi.org/10.48550/arxiv.2211.14011" @default.
- W4310403839 hasPublicationYear "2022" @default.
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