Result: A nonlinear bound for the number of subsequence sums

Title:
A nonlinear bound for the number of subsequence sums
Authors:
Lev, Vsevolod F.
Source:
European Journal of Combinatorics. 118:103907
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 2024.
Publication Year:
2024
Subject Terms:
subset sums, Mathematics - Number Theory, Inverse problems of additive number theory, including sumsets, zero-sum-free sequences, 0102 computer and information sciences, 01 natural sciences, minimal zero-sum sequences, inverse zero-sum problems, Additive bases, including sumsets, Other combinatorial number theory, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO), 0101 mathematics
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
0195-6698
DOI:
10.1016/j.ejc.2023.103907
DOI:
10.48550/arxiv.2212.10377
Access URL:
http://arxiv.org/abs/2212.10377
Rights:
Elsevier TDM
CC BY
Accession Number:
edsair.doi.dedup.....a976b0f9227a1c90ebec24f401892533
Database:
OpenAIRE

Further Information

We show that a finite zero-sum-free sequence $α$ over an abelian group has at least $c|α|^{4/3}$ distinct subsequence sums, unless $α$ is "controlled" by a small number of its terms; here $|α|$ denotes the number of terms of $α$, and $c>0$ is an absolute constant.