Results 1 to 10 of about 34,821 (85)
Computation of Gordian distances and H2-Gordian distances of knots [PDF]
Yugoslav Journal of Operations Research, 2015 One of the most complicated problems in Knot theory is to compute unknotting number. Hass, Lagarias and Pippenger proved that the unknotting problem is NP hard.
Zeković Ana
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Knot topology of exceptional point and non-Hermitian no-go theorem
Physical Review Research, 2022 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.
Haiping Hu, Shikang Sun, Shu Chen
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Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots [PDF]
, 2015 We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to
Audoly, B. +3 more
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Chirality of Knots $9_{42}$ and $10_{71}$ and Chern-Simons Theory [PDF]
, 1994 Upto ten crossing number, there are two knots, $9_{42}$ and $10_{71}$ whose chirality is not detected by any of the known polynomials, namely, Jones invariants and their two variable generalisations, HOMFLY and Kauffman invariants.
Govindarajan, T. R. +2 more
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, 2005 In the present paper, we describe new approaches for constructing virtual knot invariants. The main background of this paper comes from formulating and bringing together the ideas of biquandle (Kauffman and Radford) the virtual quandle (Manturov), the ...
Kauffman, Louis +1 more
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Introduction to disoriented knot theory
Open Mathematics, 2018 This paper is an introduction to disoriented knot theory, which is a generalization of the oriented knot and link diagrams and an exposition of new ideas and constructions, including the basic definitions and concepts such as disoriented knot ...
Altıntaş İsmet
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Tile Number and Space-Efficient Knot Mosaics [PDF]
, 2017 In this paper we introduce the concept of a space-efficient knot mosaic. That is, we seek to determine how to create knot mosaics using the least number of non-blank tiles necessary to depict the knot.
Adams +48 more
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Nature Communications, 2019 For interlocking ring structures, knot theory predicts that the number of topologically different links increases with ring and crossing number. Here, the authors use a peptide folding-and-assembly strategy to selectively realize two highly entangled ...
Tomohisa Sawada +5 more
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The forbidden number of a knot [PDF]
, 2014 Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the {\it forbidden
Crans, Alissa +2 more
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Legendrian and transverse twist knots
, 2011 In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the $m(5_2)$ knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least $n$ different Legendrian representatives with maximal Thurston--Bennequin ...
Etnyre, John B. +2 more
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