A Weighted Generalization of Gao's <i>n</i> + <i>D</i> − 1 Theorem

Abstract

Let G denote a finite abelian group of order n and Davenport constant D , and put m = n + D − 1. Let x = ( x 1 ,. . ., x m ) ∈ G m . Gao's theorem states that there is a reordering ( x j 1 , . . ., x j m ) of x such that Let w = ( x 1 , . . ., w m ) ∈ ℤ m . As a corollary of the main result, we show that there are reorderings ( x j 1 , . . ., x j m ) of x and ( w k 1 , . . ., w k m ) of w , such that where x j 1 is the most repeated value in x . For w = (1, . . ., 1), this result reduces to Gao's theorem.

Locations

• arXiv (Cornell University) - View - PDF
• Combinatorics Probability Computing - View