Square-weighted zero-sum constants

2022/02/26 by Krishnendu Sekhar Paul, Paul, Krishnendu, Shameek Paul +1
Mathematics · #11B50 (primary) #11B75 (secondary) #Advanced Topology and Set Theory #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2202.13143

openalex publication_date 2022/02/26 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

Let A⊆ \mathbb Z_n be a subset. A sequence S=(x₁,…,x_k) in \mathbb Z_n is said to be an A-weighted zero-sum sequence if there exist a₁,…,a_k∈ A such that a₁x₁+⋯+a_kx_k=0. By a square, we shall mean a non-zero square in \mathbb Z_n. We determine the smallest natural number k, such that every sequence in \mathbb Z_n whose length is k, has a square-weighted zero-sum subsequence. We also determine the smallest natural number k, such that every sequence in \mathbb Z_n whose length is k, has a square-weighted zero-sum subsequence whose terms are consecutive terms of the given sequence.

Related

• Doubly-weighted zero-sum constants
• Extremal Sequences for a Weighted Zero-Sum Constant
• On unit-weighted zero-sum constants of \mathbb Z_n
• Zero-sum constants related to the Jacobi symbol
• A zero-sum theorem over Z