Equipartitions of Mass Distributions by Orthogonal Hyperplanes and Regular m-Fans

Details Equipartitions of Mass Distributions by Orthogonal Hyperplanes and Regular m-Fans Equipartitions of Mass Distributions by Orthogonal Hyperplanes and Regular m-Fans

2010-11-08

arxiv.org/abs/1011.1922v4

Mathematics

Combinatorics

14 pages

Scientific paper

We consider the problem of finding pairwise orthogonal hyperplanes and regular m-fans which equipartition a given collection of mass distributions, with results obtained by examining the geometric topology of real projective space in the case of hyperplanes and of lens spaces in the case of regular m-fans, m>2. For example, the parallelizability of RP^3 and RP^7 is used to show that any two mass distributions on R^4 or R^8 can be bisected by 3 or 7 pairwise orthogonal hyperplanes, while a study of the lens spaces L^3(3) and L^3(4) yields that any mass distribution on R^4 can be equipartitioned by a pair of orthogonal regular 3-fans and by a pair of orthogonal regular 4-fans.

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