On some weighted zero-sum constants II

Mohan Chintamani, Prabal Paul

Type: Article

Publication Date: 2017-08-06

Citations: 3

DOI: https://doi.org/10.1142/s1793042118500264

Abstract

For a finite abelian group [Formula: see text] with exponent [Formula: see text], let [Formula: see text]. The constant [Formula: see text] (respectively [Formula: see text]) is defined to be the least positive integer [Formula: see text] such that given any sequence [Formula: see text] over [Formula: see text] with length [Formula: see text] has a [Formula: see text]-weighted zero-sum subsequence of length [Formula: see text] (respectively at most [Formula: see text]). In [M. N. Chintamani and P. Paul, On some weighted zero-sum constants, Int. J. Number Theory 13(2) (2017) 301–308], we proved the exact value of this constant for the group [Formula: see text] and proved the structure theorem for the extremal sequences related to this constant. In this paper, we prove the similar results for the group [Formula: see text] and we obtained an upper bound when [Formula: see text] is replaced by any integer [Formula: see text].

Locations

International Journal of Number Theory - View - PDF

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