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arXiv · 2609.26033

Factorisability of Low Dimensional Non-Negative Integer Matrices

Paul C. Bell·Eva Foster·Daniel Reidenbach·Pavel Semukhin
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Abstract

We consider the problem of determining if a given two-dimensional nonnegative integer matrix $M$ is the product of two such matrices, excluding trivial units. A matrix $M$ with no such factorisation is called prime and therefore belongs to the minimal (infinite rank) generator of $2 \times 2$ matrices over the natural numbers, otherwise it is called composite. We also consider the problem of finding a (non-unique) factorisation of a composite matrix. Our results have applications in computational group theory and the theory of codes, where such matrices are called incidence matrices. We analyse the complexity of primality and finding a factorisation for a composite matrix, providing a first efficient algorithm.

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BibTeXRIS

Paul C. Bell, Eva Foster, Daniel Reidenbach, Pavel Semukhin. 2026-09-22. Factorisability of Low Dimensional Non-Negative Integer Matrices. https://arxiv.org/abs/2609.26033

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