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Jerrold R. Griggs and Günter Rote:

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On the distribution of sums of vectors in general position

*In: "Contemporary Trends in Discrete Mathematics." Editors: Ronald L.
Graham, Jan Kratochvíl, Jaroslav Nešetřil, and Fred S. Roberts.
DIMACS series in discrete mathematics and theoretical computer science,
American Mathematical Society, 1999; pp. 139-142.*
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Abstract

An analog of the Littlewood-Offord problem that was posed by the first
author is to find the maximum number of subset sums equal to the same vector
over all ways of selecting *n* vectors in *R*^{d} in
general position. This note reviews past progress and motivation for this
problem, and presents a construction that gives a respectable new lower
bound, Omega(2^{n}n^{1-3d/2}), which compares
for *d*>1 to the previously known upper bound *O*(2^{n}n^{-1-d/2}).
Last update: April 5, 2002.