4 papers
On the integer partitions recursive structure
Boris Y. Rubinstein
Sylvester showed that the partition of an integer into a set of positive integers can be represented as a sum of the polynomial term and quasiperiodic components called the Sylvest…
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…
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…
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…