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#### Balanced partitions of vector sequences

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##### Citation

Bárány, I., & Doerr, B. (2006). Balanced partitions of vector sequences.*
Linear Algebra and its Applications,* *414*, 464-469.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-223D-3

##### Abstract

Let and · be any norm on . Let B denote the unit ball with respect to this
norm. We show that any sequence v1, v2, … of vectors in B can be partitioned
into r subsequences V1, …, Vr in a balanced manner with respect to the partial
sums: For all , we have . A similar bound holds for partitioning sequences of
vector sets. Both results extend an earlier one of Bárány and Grinberg [I.
Bárány, V.S. Grinberg, On some combinatorial questions in finite-dimensional
spaces, Linear Algebra Appl. 41 (1981) 1–9] to partitions in arbitrarily many
classes.