A Note on Masspartitions by Hyperplanes

TL;DR

This paper refines the understanding of mass partition problems by hyperplanes, providing a comprehensive classification of admissible parameters through elementary reductions and existing results.

Contribution

It offers a new elementary reduction method that, combined with Ramos's results, classifies all known admissible triples with one exception.

Findings

Classified all known admissible triples with one exception

Introduced an elementary reduction technique for mass partition problems

Extended the set of known admissible parameters

Abstract

A triple of positive integers (d,h,m) is admissible if for any m given masses in R^d there exist h hyperplanes that cut each of these masses into 2^h equal pieces. We present an elementary reduction which combined with results by Ramos (1996) yields all the admissible triples that were known up to now (with one exception) as well as new ones.