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Block partitions of sequences

Wednesday 19 November 2014
Imre Bárány
4pm - 5pm, 32L.G.20, LSE

Abstract

Given a sequence A=(a_1,...,a_n) of real numbers, a block B of A is either a set B={a_i,a_{i+1},...,a_j}  where i <= j or the empty set. The size b of a block B is the sum of its elements. We show that when each a_i  lies in [0,1] and k is a positive integer, then there is a partition of A into k blocks B_1,...,B_k such that |b_i-b_j| is at most one for every i,j. We extend this result in several directions. 

This is joint work with Victor Grinberg.

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