Results 1 to 10 of about 38,049 (200)
The average genus of oriented rational links with a given crossing number [PDF]
Journal of knot theory and its ramifications, 2022 . In this paper, we enumerate the number of oriented rational knots and the number of oriented rational links with any given crossing number and minimum genus.
Dawn Ray, Y. Diao
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Strict Inequalities for the n-crossing Number [PDF]
Journal of knot theory and its ramifications, 2022 In 2013, Adams introduced the $n$-crossing number of a knot $K$, denoted by $c_n(K)$. Inequalities between the $2$-, $3$-, $4$-, and $5$-crossing numbers have been previously established.
Nicholas Hagedorn
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Ribbonlength and crossing number for folded ribbon knots [PDF]
Journal of knot theory and its ramifications, 2020 We study Kauffman’s model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The ribbonlength is the length to width ratio of such a folded ribbon knot.
E. Denne
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On the braid index of a two-bridge knot [PDF]
Journal of knot theory and its ramifications, 2023 In this paper, we consider two properties on the braid index of a two-bridge knot. We prove an inequality on the braid indices of two-bridge knots if there exists an epimorphism between their knot groups.
Masaaki Suzuki, Anh T. Tran
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Connected sum and crossing numbers of flat virtual knots [PDF]
Journal of knot theory and its ramifications, 2023 The connected sum of two flat virtual knots depends on the choice of diagrams and basepoints. We show that any minimal crossing diagram of a composite flat virtual knot is a connected sum diagram. We also show the crossing number of flat virtual knots is
Jie Chen
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Link Crossing Number is NP-hard [PDF]
Journal of knot theory and its ramifications, 2019 We show that determining the crossing number of a link is NP-hard. For some weaker notions of link equivalence, we also show NP-completeness.
A. D. Mesmay, M. Schaefer, E. Sedgwick
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Triple crossing number and double crossing braid index [PDF]
Journal of knot theory and its ramifications, 2018 Traditionally, knot theorists have considered projections of knots where there are two strands meeting at every crossing. A triple crossing is a crossing where three strands meet at a single point, such that each strand bisects the crossing.
Daishiro Nishida
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Knot topology of exceptional point and non-Hermitian no-go theorem [PDF]
, 2021 Exceptional points (EPs) are peculiar band singularities and play a vital role in a rich array of unusual optical phenomena and non-Hermitian band theory. In this paper, we provide a topological classification of isolated EPs based on homotopy theory.
Haiping Hu, Shi-Kang Sun, Shu Chen
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Triple-crossing number and moves on triple-crossing link diagrams [PDF]
Journal of knot theory and its ramifications, 2017 Every link in the 3-sphere has a projection to the plane where the only singularities are pairwise transverse triple points. The associated diagram, with height information at each triple point, is a triple-crossing diagram of the link.
C. Adams, J. Hoste, Martin Palmer
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A lower bound on the average genus of a 2-bridge knot [PDF]
Journal of knot theory and its ramifications, 2021 Experimental data from Dunfield et al using random grid diagrams suggests that the genus of a knot grows linearly with respect to the crossing number. Using billiard table diagrams of Chebyshev knots developed by Koseleff and Pecker and a random model of
Moshe Cohen
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