### Abstract

We are given n boxes, labeled 1, 2,..., n. Box i weighs i grams and can support a total weight of i grams. The number of different ways to build a single stack of boxes in which no box will be squashed by the weight of the boxes above it is denoted by f(n). In a 2006 paper, the first author asked for "congruences for f(n) modulo high powers of 2". In this note, we accomplish this task by proving that, for r ≥ 5 and all n ≥ 0, f(2
^{r}
n) - f(2
^{r-1}
n) ≡ 0 (mod 2
^{r}
), and that this result is "best possible". Some additional complementary congruence results are also given.

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

Pages (from-to) | 255-263 |

Number of pages | 9 |

Journal | Australasian Journal of Combinatorics |

Volume | 44 |

State | Published - Jun 1 2009 |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics

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## Cite this

*Australasian Journal of Combinatorics*,

*44*, 255-263.