Equipartitions of a mass in boxes

https://doi.org/10.1016/j.jcta.2008.04.009Get rights and content
Under an Elsevier user license
open archive

Abstract

The aim of this paper is to provide the sufficient condition for a mass distribution in Rd to admit an equipartition with a collection of hyperplanes some of which are parallel. The results extend the previously obtained results for the equipartitions with non-parallel hyperplanes. (See [P. Mani-Levitska, S. Vrećica, R. Živaljević, Topology and combinatorics of partitions of masses by hyperplanes, Adv. Math. 207 (2006) 266–296; E.A. Ramos, Equipartitions of mass distributions by hyperplanes, Discrete Comput. Geom. 15 (1996) 147–167].)

The paper also serves as the illustration of the applicability and the power of the methods of equivariant topology (more precisely, equivariant index theory) in the problems of geometric combinatorics.

Keywords

Ideal-valued cohomological index theory

Cited by (0)

1

Supported by the Serbian Ministry of Science, Grant 144026.