On Cayley algorithm for double partition Article Swipe

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Diophantine equation Partition (number theory) Mathematics Integer (computer science) Partition problem Reduction (mathematics) Scalar (mathematics) Combinatorics Discrete mathematics Algorithm Computer science Geometry Programming language

Boris Rubinstein ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2310.00538 · OA: W4387323598

A double partition problem asks for a number of nonnegative integer solutions to a system of two linear Diophantine equations with integer coefficients. Artur Cayley suggested a reduction of a double partition to a sum of scalar partitions with an algorithm subject to a set of conditions. We show that when these conditions are not satisfied and the original algorithm fails its modification solves the reduction problem.