Results 11 to 20 of about 38,049 (200)
Lower bounds for the warping degree of a knot projection [PDF]
Journal of knot theory and its ramifications, 2021 The warping degree of an oriented knot diagram is the minimal number of crossings which we meet as an under-crossing first when we travel along the diagram from a fixed point.
Atsushi Ohya, Ayaka Shimizu
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On inequalities between unknotting numbers and crossing numbers of spatial embeddings of trivializable graphs and handlebody-knots [PDF]
Journal of knot theory and its ramifications, 2021 We study relations between the unknotting number and the crossing number of a spatial embedding of a handcuff-graph and a theta curve. It is well known that for any non-trivial knot [Formula: see text] twice the unknotting number of [Formula: see text ...
Yuta Akimoto
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Remarks on Suzuki’s knot epimorphism number [PDF]
Journal of knot theory and its ramifications, 2018 A partial order on prime knots can be defined by declaring [Formula: see text], if there exists an epimorphism from the knot group of [Formula: see text] onto the knot group of [Formula: see text]. Suppose that [Formula: see text] is a 2-bridge knot that
J. Hoste +2 more
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Petal Number of Torus Knots Using Superbridge Indices [PDF]
Journal of knot theory and its ramifications, 2022 A petal projection of a knot $K$ is a projection of a knot which consists of a single multi-crossing and non-nested loops. Since a petal projection gives a sequence of natural numbers for a given knot, the petal projection is a useful model to study knot
Hyoungjun Kim, Sungjong No, Hyungkee Yoo
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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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The Stick Number of Rail ARCS [PDF]
Journal of knot theory and its ramifications, 2022 Consider two parallel lines $\ell_1$ and $\ell_2$ in $\mathbb{R}^3$. A rail arc is an embedding of an arc in $\mathbb{R}^3$ such that one endpoint is on $\ell_1$, the other is on $\ell_2$, and its interior is disjoint from $\ell_1\cup\ell_2$.
Nicholas Cazet
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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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On the Triple Point Number of Surface-Links in Yoshikawa's Table [PDF]
Journal of knot theory and its ramifications, 2022 Yoshikawa made a table of knotted surfaces in R^4 with ch-index 10 or less. This remarkable table is the first to enumerate knotted surfaces analogous to the classical prime knot table.
Nicholas Cazet
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Space Efficient Knot Mosaics for Prime Knots with Crossing Number 10 and Less [PDF]
, 2021 The study of knot mosaics is based upon representing knot diagrams using a set of tiles on a square grid. This relatively new branch of knot theory has many unanswered questions, especially regarding the efficiency with which we draw knots as mosaics ...
Canning, James
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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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