Unfolding cubes: nets, packings, partitions, chords
Combinatorics
2020-07-28 v1 Discrete Mathematics
Abstract
We show that every ridge unfolding of an -cube is without self-overlap, yielding a valid net. The results are obtained by developing machinery that translates cube unfolding into combinatorial frameworks. Moreover, the geometry of the bounding boxes of these cube nets are classified using integer partitions, as well as the combinatorics of path unfoldings seen through the lens of chord diagrams.
Cite
@article{arxiv.2007.13266,
title = {Unfolding cubes: nets, packings, partitions, chords},
author = {Kristin DeSplinter and Satyan L. Devadoss and Jordan Readyhough and Bryce Wimberly},
journal= {arXiv preprint arXiv:2007.13266},
year = {2020}
}
Comments
17 pages, 18 figures