Geodesic
Unfolding cubes: nets, packings, partitions, chords
Kristin DeSplinter1 ; Satyan Devadoss2 ; Jordan Readyhough3 ; Bryce Wimberly4
1University of Utah
2University of San Diego
3Columbia University
4Trident Analysis
The electronic journal of combinatorics, Tome 27 (2020) no. 4

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Zbl DOI arXiv
We show that every ridge unfolding of an $n$-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.
DOI : 10.37236/9796
Classification : 52B11, 52B05, 05C38
Mots-clés : \(n\)-cube, unfolding cube

Kristin DeSplinter  1   ; Satyan Devadoss  2   ; Jordan Readyhough  3   ; Bryce Wimberly  4

1 University of Utah
2 University of San Diego
3 Columbia University
4 Trident Analysis 
Kristin DeSplinter; Satyan Devadoss; Jordan Readyhough; Bryce Wimberly. Unfolding cubes: nets, packings, partitions, chords. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9796
@article{10_37236_9796,
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     title = {Unfolding cubes: nets, packings, partitions, chords},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {4},
     doi = {10.37236/9796},
     zbl = {1454.52009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9796/}
}
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