A New Class of Linear Relations for Scalar Partitions

2025/08/01 by Rubinstein, Boris Y. · 1 citation
#11P82 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.00677

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.

Citations

• On the Sylvester program and Cayley algorithm for vector partition reduction
• On Cayley algorithm for double partition
• Sylvester-Cayley vector partitions algorithm and the Gaussian polynomials
• Complete Bell polynomials and new generalized identities for polynomials of higher order
• Restricted Partition Functions as Bernoulli and Euler Polynomials of Higher Order

Cited by

• A New Class of Relations for Homogeneous Symmetric Polynomials

Related

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• On the Sylvester program and Cayley algorithm for vector partition reduction
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