Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, October 26, 2010, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Frederik von Heymann (TU Delft)

Combinatorial ideas for an old analytic enigma.

Consider a point p on the n-dimensional sphere. We can find 2^n sums by summing up the coordinates of p, where we are allowed to change the sign of every entry. Is it possible to choose p (and n) such that more than half of the sums have absolute value >1?

This question, first published in 1986, is still open and has nice interpretations in combinatorics, geometry, probability theory and other branches of mathematics. We will use the probabilistic reformulation to show that at least (3/8)th of the sums have absolute value at most 1, and the geometric reformulation to solve the problem for small dimensions.

Main source: Ron Holzman, Daniel Kleitman: On the product of sign vectors and unit vectors, Combinatorica 12 (1992).

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