Mountain Counting
On the Enumeration of Three-Dimensional Stacks of Spheres
Keywords:
enumerative combinatorics; generating functions
Abstract
We investigate the combinatorial objects of mountains of spheres, which are three-dimensional variants of two-dimensional fountains of coins. A mountain can be decomposed into a sequence of fountains, and this decomposition leads to a recurrence relation. We obtain a closed-form solution for their counts based on this recurrence relation. Lastly, we discuss the computational feasibility of this enumeration.
Published
2022-04-15
How to Cite
Thomas, A., & May, R. (2022). Mountain Counting: On the Enumeration of Three-Dimensional Stacks of Spheres. The PUMP Journal of Undergraduate Research, 5, 70-79. https://doi.org/10.46787/pump.v5i0.2664
Section
Articles
Copyright (c) 2022 Russell May, Aaron Thomas
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