### Abstract

A partition n=p1+p2+⋯+pk with 1≤p1≤p2≤⋯≤pk is called non-squashing if p1+⋯+pj≤pj+1 for 1≤j≤k-1. Hirschhorn and Sellers showed that the number of non-squashing partitions of n is equal to the number of binary partitions of n. Here we exhibit an explicit bijection between the two families, and determine the number of non-squashing partitions with distinct parts, with a specified number of parts, or with a specified maximal part. We use the results to solve a certain box-stacking problem.

Original language | English (US) |
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Pages (from-to) | 259-274 |

Number of pages | 16 |

Journal | Discrete Mathematics |

Volume | 294 |

Issue number | 3 |

DOIs | |

State | Published - May 6 2005 |

Externally published | Yes |

### Keywords

- Binary partitions
- Non-squashing partitions
- Partitions
- Stacking boxes
- m-ary Partitions

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## Cite this

Sloane, N. J. A., & Sellers, J. A. (2005). On non-squashing partitions.

*Discrete Mathematics*,*294*(3), 259-274. https://doi.org/10.1016/j.disc.2004.11.014