Description Usage Arguments Value Author(s) References See Also Examples

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`

.

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

`n` |
A positive integer to be partitioned. |

`M` |
A positive integer, the number of parts of |

`at.most` |
If |

`p.n` |
total number of partitions obtained. |

`partitions` |
a matrix with each column presenting partitions of |

Vassilly Voinov, Natalya Pya Arnqvist, Yevgeniy Voinov

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)
``` |

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