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A Weighted Generalization of Gao's n + D − 1 Theorem

Published online by Cambridge University Press:  01 November 2008

YAHYA O. HAMIDOUNE
YAHYA O. HAMIDOUNE*
Affiliation:
UPMC Université Paris 6, E. Combinatoire, Case 189, 4 Place Jussieu, 75005 Paris, France (e-mail: hamidoune@math.jussieu.fr)
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Abstract

Let G denote a finite abelian group of order n and Davenport constant D, and put m = n + D − 1. Let x = (x1,. . .,xm) ∈ Gm. Gao's theorem states that there is a reordering (xj1, . . ., xjm) of x such that

Let w = (x1, . . ., wm) ∈ ℤm. As a corollary of the main result, we show that there are reorderings (xj1, . . ., xjm) of x and (wk1, . . ., wkm) of w, such thatwhere xj1 is the most repeated value in x. For w = (1, . . ., 1), this result reduces to Gao's theorem.

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 6 , November 2008 , pp. 793 - 798
Copyright
Copyright © Cambridge University Press 2008

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