Large subsets of  Z m n without arithmetic progressions

For integers and , we study the problem of finding good lower bounds for the size of progression-free sets in . Let denote the maximal size of a subset of without arithmetic progressions of length  and let denote the least prime factor of  . We construct explicit progression-free sets and obtain the...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2023, Vol.91 (4), p.1443
Main Authors: Elsholtz, Christian, Klahn, Benjamin, Lipnik, Gabriel F
Format: Article
Language:English
Online Access:Get full text
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Summary:For integers and , we study the problem of finding good lower bounds for the size of progression-free sets in . Let denote the maximal size of a subset of without arithmetic progressions of length  and let denote the least prime factor of  . We construct explicit progression-free sets and obtain the following improved lower bounds for :If is odd and , then If is even, and , then Moreover, we give some further improved lower bounds on for primes and progression lengths .
ISSN:1573-7586
1573-7586
DOI:10.1007/s10623-022-01145-w