On some weighted zero-sum constants

Abstract

Let [Formula: see text] be a finite abelian group with exponent exp[Formula: see text]. Let [Formula: see text]. The constant [Formula: see text] is defined as the least positive integer [Formula: see text] such that for any given sequence [Formula: see text] of elements of [Formula: see text] with length [Formula: see text] it has a [Formula: see text] length [Formula: see text]-weighted zero-sum subsequence. In this article, we obtain the exact value of [Formula: see text] for [Formula: see text] and an upper bound for the case [Formula: see text], where [Formula: see text] is an odd prime, [Formula: see text] is an odd integer and [Formula: see text]. We also obtain the structural information on the extremal zero-sum free sequences.