Abstract
Recently, Sloane and Sellers solved a certain box stacking problem related to non-squashing partitions. These are defined as partitions n = p1 + p2 + ⋯ + pk with 1 ≤ p1 ≤ p2 ≤ ⋯ ≤ pk wherein p1 + ⋯ + pj ≤ pj + 1 for 1 ≤ j ≤ k - 1. Sloane has also hinted at a generalized box stacking problem which is closely related to generalized non-squashing partitions. We solve this generalized box stacking problem by obtaining a generating function for the number of such stacks and discuss partition functions which arise via this generating function.
Original language | English (US) |
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Pages (from-to) | 1185-1190 |
Number of pages | 6 |
Journal | Discrete Mathematics |
Volume | 307 |
Issue number | 9-10 |
DOIs | |
State | Published - May 6 2007 |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics