Sidon sets in a union of intervals

DOI10.1007/S10474-022-01246-XarXiv2202.01296MaRDI QIDQ6389985

Robin Riblet

Publication date: 2 February 2022

Abstract: We study the maximum size of Sidon sets in unions of integers intervals. If $AsubseteqmathbbN$ is the union of two intervals and if $left|Aight|=n$ (where $left|Aight|$ denotes the cardinality of $A$), we prove that $A$ contains a Sidon set of size at least $0,876sqrtn$. On the other hand, by using the small differences technique, we establish a bound of the maximum size of Sidon sets in the union of $k$ intervals.

Mathematics Subject Classification ID

Additive bases, including sumsets (11B13) Arithmetic combinatorics; higher degree uniformity (11B30)

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