3 papers
math.NT2025
A New Class of Linear Relations for Scalar Partitions
Boris Y. Rubinstein
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…
math.NT2025
Unbounded knapsack problem and double partitions
Boris Y. Rubinstein
The unbounded knapsack problem can be considered as a particular case of the double partition problem that asks for a number of nonnegative integer solutions to a system of two lin…
math.NT2025
On the Sylvester program and Cayley algorithm for vector partition reduction
Boris Y. Rubinstein
A vector partition problem asks for a number of nonnegative integer solutions to a system of several linear Diophantine equations with integer nonnegative coefficients. J.J. Sylves…