Counting alternating knots by genus

被引：19

作者：

Stoimenow, A

Vdovina, A

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Tokyo 1538914, Japan

[2] Newcastle Univ, Sch Math & Stat, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

来源：

MATHEMATISCHE ANNALEN | 2005年 / 333卷 / 01期

关键词：

Trivalent Graph;

D O I：

10.1007/s00208-005-0659-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that the number of alternating knots of given genus g > 1 grows as a polynomial of degree 6g - 4 in the crossing number. The leading coefficient of the polynomial, which depends on the parity of the crossing number, is related to planar trivalent graphs with a Bieulerian path. The rate of growth of the number of such graphs is estimated.

引用

页码：1 / 27

页数：27

共 50 条

[41] Periodicity and free periodicity of alternating knots
Costa, Antonio F.
Hongler, Cam Van Quach
TOPOLOGY AND ITS APPLICATIONS, 2023, 339
[42] A topological characterization of toroidally alternating knots
Kim, Seungwon
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2019, 27 (08) : 1825 - 1850
[43] Alternating knots with unknotting number one
McCoy, Duncan
ADVANCES IN MATHEMATICS, 2017, 305 : 757 - 802
[44] BPS counting for knots and combinatorics on words
Piotr Kucharski
Piotr Sułkowski
Journal of High Energy Physics, 2016
[45] BPS counting for knots and combinatorics on words
Kucharski, Piotr
Sulkowski, Piotr
JOURNAL OF HIGH ENERGY PHYSICS, 2016, (11):
[46] Counting Links and Knots in Complete Graphs
Abrams, Loren
Mellor, Blake
Trott, Lowell
TOKYO JOURNAL OF MATHEMATICS, 2013, 36 (02) : 429 - 458
[47] Knots of (canonical) genus two
Stoimenow, A.
FUNDAMENTA MATHEMATICAE, 2008, 200 (01) : 1 - 67
[48] THE ALGEBRAIC DETERMINATION OF THE GENUS OF KNOTS
NEUWIRTH, L
AMERICAN JOURNAL OF MATHEMATICS, 1960, 82 (04) : 791 - 798
[49] Additivity of free genus of knots
Ozawa, M
TOPOLOGY, 2001, 40 (04) : 659 - 665
[50] The Turaev genus of torus knots
Jin, Kaitian
Lowrance, Adam M.
Polston, Eli
Zheng, Yanjie
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2017, 26 (14)

← 1 2 3 4 5 →