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.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics