Jerrold R. Griggs and Günter Rote:
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.
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 Rd 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(2nn1-3d/2), which compares
for d>1 to the previously known upper bound O(2nn-1-d/2).
Last update: April 5, 2002.