Bipyramid Volume, Mahler Measure and Some $\mathbb{Z}^2$-periodic Links

Hong-Chuan Gan

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arXiv · 2202.10218

Bipyramid Volume, Mahler Measure and Some $\mathbb{Z}^2$-periodic Links

Hong-Chuan Gan

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Abstract

Champanerkar, Kofman and Lal\'{i}n conjectured an inequality between bipyramid volume of links and Mahler measure of associated dimer models induced from alternating links on torus. Hyperbolic volume and Mahler measure can be related for isoradial graphs, which allows us to confirm the conjecture for two examples. By exploiting a connection between perfect matchings of dimer models and spanning trees on lattices, five more examples are calculated.

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Hong-Chuan Gan. 2022-02-21. Bipyramid Volume, Mahler Measure and Some $\mathbb{Z}^2$-periodic Links. https://arxiv.org/abs/2202.10218

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