On the Partition of Space by Hyperplanes

Authors

  • Armen Bagdasaryan American University of the Middle East

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i2.4713

Keywords:

hyperplane arrangement, number of regions, binomial coefficients

Abstract

We consider the problem of partitioning of space by hyperplanes that arises in many application areas, where the number of regions the space is divided into is required to be determined, such as speech/pattern recognition, various classification problems, data analysis. We obtain some relations for the number of divisions and establish a recurrence relation for the maximum number of regions in d-dimensional Euclidean space cut by n hyperplanes. We also re-derive an explicit formula for the number of regions into which the space can be partitioned by n hyperplanes.

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Published

2023-04-30

Issue

Section

Nonlinear Analysis

How to Cite

On the Partition of Space by Hyperplanes. (2023). European Journal of Pure and Applied Mathematics, 16(2), 893-898. https://doi.org/10.29020/nybg.ejpam.v16i2.4713