Ball packings for links

被引：2

作者：

Alfonsin, Jorge L. Ramirez ^{[1
,2
]}

Rasskin, Ivan ^{[2
]}

机构：

[1] CNRS IMPA, UMI2924, Santos, Brazil

[2] Univ Montpellier, CNRS, IMAG, Montpellier, France

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2021年 / 96卷

关键词：

NUMBERS; GRAPHS;

D O I：

10.1016/j.ejc.2021.103351

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The ball number of a link L, denoted by ball(L), is the minimum number of solid balls (not necessarily of the same size) needed to realize a necklace representing L. In this paper, we show that ball(L) <= 5cr(L) where cr(L) denotes the crossing number of a nontrivial nonsplittable link L. To this end, we use the connection of the Lorentz geometry with the ball packings. The well-known Koebe-Andreev-Thurston circle packing Theorem is also an important brick for the proof. Our approach yields an algorithm to construct explicitly the desired necklace representation of L in R-3. (C) 2021 Elsevier Ltd. All rights reserved.

引用

页数：20

共 50 条

[41] Geodesic ball packings in S2 × R space for generalized Coxeter space groups
Szirmai J.
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2011, 52 (2): : 413 - 430
[42] Determination of transitive optimal ball packings for 29 space groups containing Coxeter reflections groups
Molnár, E
Prok, I
Szirmai, J
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2002, 39 (3-4) : 443 - 483
[43] THE EXTENSION OF THE VORONOI-DELAUNAY METHOD TO DESCRIBE A VOID SPACE INSIDE POLYDISPERSE BALL PACKINGS
MEDVEDEV, NN
DOKLADY AKADEMII NAUK, 1994, 337 (06) : 767 - 771
[44] Optimal ball packings for crystallographic groups of the cubic crystal system and their Dirichlet-Voronoi cells
Prok, I
Szirmai, J
ZEITSCHRIFT FUR KRISTALLOGRAPHIE, 2006, 221 (01): : 99 - 103
[45] A lower bound for the mean width of Voronoi polyhedra of unit ball packings in E3
K. Bezdek
Archiv der Mathematik, 2000, 74 : 392 - 400
[46] Geodesic and Translation Ball Packings Generated by Prismatic Tessellations of the Universal Cover of SL2(R)
Molnar, Emil
Szirmai, Jeno
Vesnin, Andrei
RESULTS IN MATHEMATICS, 2017, 71 (3-4) : 623 - 642
[47] On a stronger form of Rogers's lemma and the minimum surface area of Voronoi cells in unit ball packings
Bezdek, K
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2000, 518 : 131 - 143
[48] Geodesic ball packings in H2 x R space for generalized Coxeter space groups
Szirmai, Jeno
MATHEMATICAL COMMUNICATIONS, 2012, 17 (01) : 151 - 170
[49] Densest Geodesic Ball Packings to S2 × R space groups generated by screw motions
Benedek Schultz
Jenő Szirmai
Mediterranean Journal of Mathematics, 2016, 13 : 775 - 788
[50] OPTIMAL BALL AND HOROBALL PACKINGS GENERATED BY 3-DIMENSIONAL SIMPLY TRUNCATED COXETER ORTHOSCHEMES WITH PARALLEL FACES
Szirmai, Jeno
Yahya, Arnasli
QUAESTIONES MATHEMATICAE, 2023, 46 (05) : 1017 - 1037

← 1 2 3 4 5 →