The CW-Inequalities for Vectors in l1

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Abstract

Let l1 denote the metric space the elements of which are all sequences x=(x1, x2,...) of real numbers satisfying ∑ i=1∞ |xi|<∞. The distance d(x, y) between x and y = (y1, y2,...) is d(x,y)=∑ i=1∞ |xi−yi|. Let υ0, υ1,..., υm−1, u0, u1,...,uk-1 be a sequence of n = m + k not necessarily distinct vectors in l1, where k > 0, m = k + 2u + 1 and u ⩾ 0. We show that ∑ 0⩽i<j<m (i−j)(modm)∈{±1,±2...,±u} d(υi,υj)+∑ 0⩽i<m 0⩽j<k d(υi,uj)⩾∑ 0⩽i<j<m d(υi,υj)+∑ 0⩽i<j<k d(ui,uj). This solves a conjecture of Deza and Laurent and implies, as special cases, inequalities of Deza, Laurent, Kelly, Barahona and Mahjoub.

Original languageEnglish (US)
Pages (from-to)1-5
Number of pages5
JournalEuropean Journal of Combinatorics
Volume11
Issue number1
DOIs
StatePublished - Jan 1 1990
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

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