# get.partitions: Additive partitioning of natural numbers In nilde: Nonnegative Integer Solutions of Linear Diophantine Equations with Applications

## Description

This function solves the problem of additive partitioning of positive integers. The approach for additive partitioning is based on a generating function discussed in details in Voinov and Nikulin (1995). The function enumerates all partitions of a positive integer `n` on at most (or exactly) `M` parts, `M <= n`.

## Usage

 `1` ``` get.partitions(n, M, at.most=TRUE) ```

## Arguments

 `n` A positive integer to be partitioned. `M` A positive integer, the number of parts of `n`, `M <= n`. `at.most` If `TRUE` then partitioning of `n` into at most `M` parts, if `FALSE` then partitioning on exactly `M` parts.

## Value

 `p.n` total number of partitions obtained. `partitions` a matrix with each column presenting partitions of `n`.

## Author(s)

Vassilly Voinov, Natalya Pya Arnqvist, Yevgeniy Voinov

## References

Voinov, V. and Nikulin, M. (1995) Generating functions, problems of additive number theory, and some statistical applications. Revue Roumaine de MathÃ©matiques Pures et AppliquÃ©es, 40(2), 107-147

Voinov, V.G. and Pya, N.E. (2017) R-software for additive partitioning of positive integers. Mathematical Journal (ISSN 1682-0525) 17(1), 69-76.

`nilde-package`, `get.knapsack`, `get.subsetsum`, `nlde`
 ```1 2 3 4 5 6 7``` ```## getting all partitions of n = 8 on at most 6 parts... get.partitions(8,6,at.most=TRUE) ## getting all partitions of n = 8 on exactly 6 parts... b <- get.partitions(8,6,at.most=FALSE) b colSums(b\$partitions) ```