On non-squashing partitions
نویسندگان
چکیده
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.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 294 شماره
صفحات -
تاریخ انتشار 2005