LIPIcs.SoCG.2024.90.pdf
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Visualizing Lucas’s Hamiltonian Paths Through the Associahedron 1-Skeleton (Media Exposition)
Authors
Christopher J. Tralie 
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Volume:
40th International Symposium on Computational Geometry (SoCG 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Computational Geometry (SoCG) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-06-06
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Kacey Thien-Huu La, Jose E. Arbelo, and Christopher J. Tralie. Visualizing Lucas’s Hamiltonian Paths Through the Associahedron 1-Skeleton (Media Exposition). In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 90:1-90:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SoCG.2024.90
https://doi.org/10.4230/LIPIcs.SoCG.2024.90
Abstract
We re-examine the 1987 paper by Joan Lucas[Lucas, 1987], who showed that the edge-flip graph of convex polygon triangulations is Hamiltonian. We focus specifically on the first part of her paper on Hamiltonian paths, and we provide a simplified algorithm for that case which elucidates how to assemble a recursive subdivision that she refers to as "stacks." Finally, we provide an interactive web-based visualization of Hamiltonian paths through the stacks.
Subject Classification
ACM Subject Classification
- Human-centered computing → Visualization toolkits
- Theory of computation → Randomness, geometry and discrete structures
Keywords
- associahedron
- hamiltonian paths
- visualization
- tree rotations
- convex polygons
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References
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Michael Bostock, Vadim Ogievetsky, and Jeffrey Heer. D³ data-driven documents. IEEE Transactions on Visualization and Computer Graphics, 17(12):2301-2309, 2011.
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Joan M Lucas. The rotation graph of binary trees is hamiltonian. Journal of Algorithms, 8(4):503-535, 1987.
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Steven Roman et al. An introduction to Catalan numbers. Springer, 2015.
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David Zerling. Generating binary trees using rotations. Journal of the ACM (JACM), 32(3):694-701, 1985.