To the Steinitz lemma in coordinate form

✍ Scribed by Sergey Sevast'janov; Wojciech Banaszczyk

• Book ID: 103060395
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 331 KB
• Volume: 169
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(94)00240-j

✦ Synopsis

We consider an arbitrary finite family of vectors in m-dimensional space with sum zero and the absolute value of any vector's coordinate at most 1. We prove that there exists an order of vector summation for this family such that the absolute value of the first coordinate for all partial sums is at most 1 while those of other coordinates are bounded by a constant independent of the family.