On the Partition of Space by Hyperplanes

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...

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Bibliographic Details
Published in:European journal of pure and applied mathematics 2023-04, Vol.16 (2), p.893-898
Main Author: Bagdasaryan, Armen
Format: Article
Language:English
Online Access:Get full text
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Summary: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.
ISSN:1307-5543
1307-5543
DOI:10.29020/nybg.ejpam.v16i2.4713