On a different weighted zero-sum constant

DOI10.1016/J.DISC.2023.113350arXiv2110.02539MaRDI QIDQ6379517

Krishnendu Paul, Santanu Mondal, Shameek Paul

Publication date: 6 October 2021

Abstract: For a finite abelian group $(G,+)$, the constant $C(G)$ is defined to be the smallest natural number $k$ such that any sequence in $G$ having length $k$ will have a subsequence of consecutive terms whose sum is zero. For a subset $Asubseteqmathbb{Z}_n$, the constant $C_A(n)$ is the smallest natural number $k$ such that any sequence in $G$ having length $k$ has an $A$-weighted zero-sum subsequence of consecutive terms. We determine the value of $C_A(n)$ for some particular weight-sets $A$.

Mathematics Subject Classification ID

Sequences (mod (m)) (11B50) Inverse problems of additive number theory, including sumsets (11P70) Combinatorial aspects of groups and algebras (05E16)

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