Long zero-free sequences in finite cyclic groups

2006/02/25 by Svetoslav Savchev, Fang Chen, Savchev, Svetoslav +1
Computer Science · Mathematics · #11B50 #11P21 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0602568

openalex publication_date 2006/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A sequence in an additively written abelian group is called zero-free if each of its nonempty subsequences has sum different from the zero element of the group. The article determines the structure of the zero-free sequences with lengths greater than n/2 in the additive group \Zn/ of integers modulo n. The main result states that for each zero-free sequence (a_i)_i=1^ℓ of length ℓ>n/2 in \Zn/ there is an integer g coprime to n such that if ga_i denotes the least positive integer in the congruence class ga_i (modulo n), then Σ_i=1^ℓga_i

Related

• Long n-zero-free sequences in finite cyclic groups
• The subsums of zero-sum free sequences in finite cyclic groups
• Zero-sum-free sequences with few subsequence sums
• Subsequence Sums of Zero-sum free Sequences II
• A note on the number of distinct elements and zero-sum subsequence lengths in cyclic groups