Measure Partitions Using Hyperplanes with Fixed Directions
Metric Geometry
2014-10-14 v5 Combinatorics
Abstract
We study nested partitions of obtained by successive cuts using hyperplanes with fixed directions. We establish the number of measures that can be split evenly simultaneously by taking a partition of this kind and then distributing the parts among sets. This generalises classical necklace splitting results and their more recent high-dimensional versions. With similar methods we show that in the plane, for any measures there is a path formed only by horizontal and vertical segments using at most turns that splits them by half simultaneously, and optimal mass-partitioning results for chessboard-colourings of using hyperplanes with fixed directions.
Cite
@article{arxiv.1408.4830,
title = {Measure Partitions Using Hyperplanes with Fixed Directions},
author = {Roman Karasev and Edgardo Roldán-Pensado and Pablo Soberón},
journal= {arXiv preprint arXiv:1408.4830},
year = {2014}
}