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Minimum number of additive tuples in groups of prime order

Abstract:

For a prime number p and a sequence of integers a0,…,ak∈{0,1,…,p}, let s(a0,…,ak) be the minimum number of (k+1)-tuples (x0,…,xk)∈A0×⋯×Ak with x0=x1+⋯+xk, over subsets A0,…,Ak⊆Zp of sizes a0,…,ak respectively. We observe that an elegant argument of Samotij and Sudakov can be extended to show that there exists an extremal configuration with all sets Ai being intervals of appropriate length. The same conclusion also holds for the related problem, posed by Bajnok, when a0=⋯=ak=:a and A0=⋯=Ak, pr...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-9968-9148
Publisher:
Electronic Journal of Combinatorics Publisher's website
Journal:
The Electronic Journal of Combinations Journal website
Volume:
26
Issue:
1
Pages:
Article: P1.30
Publication date:
2019-02-22
Acceptance date:
2019-01-30
ISSN:
1077-8926
Pubs id:
pubs:820649
URN:
uri:0852dfd6-7860-4892-8b05-2cdf6fe33984
UUID:
uuid:0852dfd6-7860-4892-8b05-2cdf6fe33984
Local pid:
pubs:820649

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