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arXiv · 2508.00677

A New Class of Linear Relations for Scalar Partitions

Boris Y. Rubinstein
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Abstract

A scalar integer partition problem asks for a number of nonnegative integer solutions to a linear Diophantine equation with integer positive coefficients. The manuscript discusses an algorithm of derivation of linear relations involving the finite number of scalar partitions. The algorithm employs the Cayley theorem about the reduction of a double partition to a sum of scalar partitions based on the variable elimination procedure.

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Boris Y. Rubinstein. 2025-08-01. A New Class of Linear Relations for Scalar Partitions. https://arxiv.org/abs/2508.00677

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