Article Dans Une Revue European Journal of Combinatorics Année : 2024

Links in orthoplicial Apollonian packings

Résumé

In this paper, we establish a connection between Apollonian packings and knot theory. We introduce new representations of links realized in the tangency graph of the regular crystallographic sphere packings. Particularly, we prove that any algebraic link can be realized in the cubic section of the orthoplicial Apollonian packing. We use these representations to improve the upper bound on the ball number of an infinite family of alternating algebraic links. Furthermore, the later allow us to reinterpret the correspondence of rational tangles and rational numbers and to reveal geometrically primitive solutions for the Diophantine equation x4 + y4 + z4 = 2t2.

HAL

A comme version hal-04527276 Preprint Jorge Luis RAMIREZ ALFONSIN, Ivan Rasskin. LINKS IN ORTHOPLICIAL APOLLONIAN PACKINGS. 2024. ⟨hal-04527276⟩

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Dates et versions

hal-05074837 , version 1 (20-05-2025)

Identifiants

Citer

Jorge Ramírez Alfonsín, Iván Rasskin. Links in orthoplicial Apollonian packings. European Journal of Combinatorics, 2024, 122, pp.104017. ⟨10.1016/j.ejc.2024.104017⟩. ⟨hal-05074837⟩
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