WebNov 3, 2024 · For instance, Dynnikov diagrams with vertical and horizontal lines can be used to represent and solve knots; these are called “arc-presentations” and their complexity is equivalent to the number of the vertical lines of the diagram and, following a theorem by Dynnikov , every knot has an arc-presentation (Fig. 17.4). WebAs an application, we determine the arc index of infinitely many Kanenobu knots. In particular, we give sharper lower bounds of the arc index of K ( 2 n, − 2 n) by using canonical cabling algorithm and the 2-cable Γ -polynomials. Moreover, we give sharper upper bounds of the arc index of some Kanenobu knots by using their braid presentations.
The problem of detecting the satellite structure of a link by …
WebAbstract Let L be a Montesinos link M ( − p, q, r) with positive rational numbers p, q and r, each less than 1, and c ( L) the minimal crossing number of L. Herein, we construct arc … WebThis SRS’s primary responsibilities include leadership and close collaboration with education researchers within ARC and across NORC to develop new research projects, design and … daily move goal
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WebJun 26, 2024 · Grid diagrams were first introduced by Cromwell, Dynnikov and Brunn [2,3,4] and have gained popularity since the use of grids to give a combinatorial definition of … WebJul 10, 2024 · We introduce a new very large family of transformations of rectangular diagrams of links that preserve the isotopy class of the link. We provide an example when two diagrams of the same complexity are related by such a transformation and are not obtained from one another by any sequence of “simpler” moves not increasing the … WebEssential tori in link complements: detecting the satellite structure by monotonic simplification A. Kazantsev1 Abstract. In a recent work “Arc-presentation of links: Monotonic sim-plification” Ivan Dynnikov showed that each rectangular diagram of the un-knot, composite link, or split link can be monotonically simplified into a triv- daily movers