On Cayley algorithm for double partition

2023/10/01 by Boris Rubinstein, Rubinstein, Boris · 2 citations
Computer Science · Mathematics · #11P82 #Algorithm #Combinatorics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Computer science #Diophantine equation #Discrete mathematics #FOS: Mathematics #Integer (computer science) #Mathematics #Number Theory (math.NT) #Partition (number theory) #Partition problem #Reduction (mathematics) #Scalar (mathematics) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2310.00538

openalex publication_date 2023/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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• A New Class of Linear Relations for Scalar Partitions
• Unbounded knapsack problem and double partitions

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