A Snevily-type inequality for multisets

Alon [1] proved that if p is an odd prime, 1 ≤ n < p and a 1 , … , a n are distinct elements in Z p and b 1 , … , b n are arbitrary elements in Z p then there exists a permutation of σ of the indices 1 , … , n such that the elements a 1 + b σ ( 1 ) , … , a n + b σ ( n ) are distinct. In this pape...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2021-06, Vol.164 (1), p.46-50
Main Authors: Gáspár, A., Kós, G.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Permutations
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Summary:Alon [1] proved that if p is an odd prime, 1 ≤ n < p and a 1 , … , a n are distinct elements in Z p and b 1 , … , b n are arbitrary elements in Z p then there exists a permutation of σ of the indices 1 , … , n such that the elements a 1 + b σ ( 1 ) , … , a n + b σ ( n ) are distinct. In this paper we present a multiset variant of this result.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-020-01123-5