### Abstract

Motivated by recent work of Bessenrodt, Olsson, and Sellers on unique path partitions, we consider partitions of an integer n wherein the parts are all powers of a fixed integer m≥ 2 and there are no "gaps" in the parts; that is, if m^{i} is the largest part in a given partition, then m^{j} also appears as a part in the partition for each 0 ≤ j< i. Our ultimate goal is to prove an infinite family of congruences modulo powers of m which are satisfied by these functions.

Original language | English (US) |
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Pages (from-to) | 495-506 |

Number of pages | 12 |

Journal | Annals of Combinatorics |

Volume | 21 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2017 |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics

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## Cite this

Andrews, G. E., Brietzke, E., Rødseth, Ø. J., & Sellers, J. A. (2017). Arithmetic Properties of m-ary Partitions Without Gaps.

*Annals of Combinatorics*,*21*(4), 495-506. https://doi.org/10.1007/s00026-017-0369-6