The Warping Degree of a Knot Diagram

Shimizu, Ayaka

doi:10.1142/s0218216510008194

Cited by 34 publications

(30 citation statements)

References 12 publications

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“…To obtain an upper bound on the unknotting index, we define warping degree for virtual links. In [11], A. Shimizu defined warping crossing points for a link diagram. Here we use the same terminology for virtual links.…”

Section: Preliminariesmentioning

confidence: 99%

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An unknotting index for virtual links

Kaur

Prabhakar

Vesnin

2019

Topology and its Applications

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Given a virtual link diagram D, we define its unknotting index U (D) to be minimum among (m, n) tuples, where m stands for the number of crossings virtualized and n stands for the number of classical crossing changes, to obtain a trivial link diagram. By using span of a diagram and linking number of a diagram we provide a lower bound for unknotting index of a virtual link. Then using warping degree of a diagram, we obtain an upper bound. Both these bounds are applied to find unknotting index for virtual links obtained from pretzel links by virtualizing some crossings.2010 Mathematics Subject Classification. Primary 57M25; Secondary 57M90.

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Section: Preliminariesmentioning

confidence: 99%

“…Example 3.1. Let L be a virtual link diagram obtained from L (7,5,9,11) pretzel link by virtualizing 13 crossings as shown in Fig. 11(a).…”

Section: Unknotting Index For Virtual Pretzel Linksmentioning

confidence: 99%

An unknotting index for virtual links

Kaur

Prabhakar

Vesnin

2019

Topology and its Applications

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“…[22], S. Fujimura [4], T. S. Fung [5], M. Okuda [26] and M. Ozawa [27] considering the ascending number of an oriented link. A. Shimizu [29,30] also established a relationship between the warping degrees and the crossing number of a knot or link diagram. In particular, A. Shimizu characterized the alternating knot diagrams by establishing the inequality…”

Section: A Monotone Diagram the Warping Degree The Complexity And Tmentioning

confidence: 99%

Knot Theory for Spatial Graphs Attached to a Surface

Kawauchi¹

2016

Contemporary Mathematics

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“…Warping span. Shimizu [Shi10,Shi11] defines the warping degree of a knot or link diagram and uses warping degree to define the warping polynomial of a knot diagram [Shi12]. She defines the span of a knot K, denoted spn(K), to be the minimum span of the warping polynomial for any diagram of K. We define a related invariant, called the warping span of K, that is essentially a renormalization of the span of the warping polynomial.…”

Section: 3mentioning

confidence: 99%