On the partition of R^n by hyperplanes

TL;DR

This paper explores how hyperplanes partition n-dimensional space, deriving formulas and recurrence relations to determine the maximum number of regions created, which is fundamental for understanding discrete classification boundaries.

Contribution

It provides a new recurrence relation and rederives an explicit formula for the maximum number of partitions of R^n by m hyperplanes, enhancing theoretical understanding.

Findings

Derived a recurrence relation for the maximum number of partitions

Reestablished the explicit formula for the number of partitions

Analyzed the relation between hyperplanes and space partitioning

Abstract

The partitioning of space by hyperplanes in the context of discrete classification problem is considered. We obtain some relations for the number of partitions and establish a recurrence relation for the maximal number of partitions of R^n by m hyperplanes. We rederive an explicit formula for the number of components into which the space can be partitioned by m hyperplanes.