### Abstract

We discuss a family of restricted m-ary partition functions b_{m,j}(n), which is the number of m-ary partitions of n with at most i + j copies of the part m^{i} allowed. We then use generating function dissections to prove the following family of congruences for k ≥ 2 and 1≤t≤m-k + 1: b_{m,m-1}(m^{k+1}n + m^{k+t-1} + m^{k+t-2} + ⋯ + m^{k}) ≡ 0 (mod 2^{t-1}k).

Original language | English (US) |
---|---|

Pages (from-to) | 265-269 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 219 |

Issue number | 1-3 |

DOIs | |

State | Published - May 28 2000 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Mathematics*,

*219*(1-3), 265-269. https://doi.org/10.1016/S0012-365X(00)00024-8

}

*Discrete Mathematics*, vol. 219, no. 1-3, pp. 265-269. https://doi.org/10.1016/S0012-365X(00)00024-8

**Congruences for a restricted m-ary partition function.** / Dolph, Laura L.; Reynolds, Annmarie; Sellers, James Allen.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Congruences for a restricted m-ary partition function

AU - Dolph, Laura L.

AU - Reynolds, Annmarie

AU - Sellers, James Allen

PY - 2000/5/28

Y1 - 2000/5/28

N2 - We discuss a family of restricted m-ary partition functions bm,j(n), which is the number of m-ary partitions of n with at most i + j copies of the part mi allowed. We then use generating function dissections to prove the following family of congruences for k ≥ 2 and 1≤t≤m-k + 1: bm,m-1(mk+1n + mk+t-1 + mk+t-2 + ⋯ + mk) ≡ 0 (mod 2t-1k).

AB - We discuss a family of restricted m-ary partition functions bm,j(n), which is the number of m-ary partitions of n with at most i + j copies of the part mi allowed. We then use generating function dissections to prove the following family of congruences for k ≥ 2 and 1≤t≤m-k + 1: bm,m-1(mk+1n + mk+t-1 + mk+t-2 + ⋯ + mk) ≡ 0 (mod 2t-1k).

UR - http://www.scopus.com/inward/record.url?scp=0347646987&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347646987&partnerID=8YFLogxK

U2 - 10.1016/S0012-365X(00)00024-8

DO - 10.1016/S0012-365X(00)00024-8

M3 - Article

AN - SCOPUS:0347646987

VL - 219

SP - 265

EP - 269

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -