Zobrazeno 1 - 10
of 81
pro vyhledávání: '"57K10, 57K14"'
Autor:
Adnan, Park, Kyungbae
Twisted torus knots are a generalization of torus knots, obtained by introducing additional full twists to adjacent strands of the torus knots. In this article, we present an explicit formula for the Alexander polynomial of twisted torus knots. Our a
Externí odkaz:
http://arxiv.org/abs/2411.13003
In this paper, we present a novel method to compute the determinant of a link using Fourier-Hadamard transforms of Boolean functions. We also investigate the determinant of centrally symmetric links (a special class of strong achiral links). In parti
Externí odkaz:
http://arxiv.org/abs/2409.14133
Autor:
Applebaum, Taylor, Blackwell, Sam, Davies, Alex, Edlich, Thomas, Juhász, András, Lackenby, Marc, Tomašev, Nenad, Zheng, Daniel
We have developed a reinforcement learning agent that often finds a minimal sequence of unknotting crossing changes for a knot diagram with up to 200 crossings, hence giving an upper bound on the unknotting number. We have used this to determine the
Externí odkaz:
http://arxiv.org/abs/2409.09032
In the study of ribbon knots, Lamm introduced symmetric unions inspired by earlier work of Kinoshita and Terasaka. We show an identity between the twisted Alexander polynomials of a symmetric union and its partial knot. As a corollary, we obtain an i
Externí odkaz:
http://arxiv.org/abs/2407.09881
We investigate Fox's trapezoidal conjecture for alternating links. We show that it holds for diagrammatic Murasugi sums of special alternating links, where all sums involved have length less than three (which includes diagrammatic plumbing). It also
Externí odkaz:
http://arxiv.org/abs/2406.08662
Autor:
Baker, Kenneth L., Motegi, Kimihiko
Twisting a given knot $K$ about an unknotted circle $c$ a full $n \in \mathbb{N}$ times, we obtain a "twist family" of knots $\{ K_n \}$. Work of Kouno-Motegi-Shibuya implies that for a non-trivial twist family the crossing numbers $\{c(K_n)\}$ of th
Externí odkaz:
http://arxiv.org/abs/2404.05308
Autor:
Qazaqzeh, Khaled, Chbili, Nafaa
We show that a link is adequate if the breadth of its Jones polynomial equals the difference between its crossing number and its Turaev genus. Combining this result with its converse obtained by Abe [1, Theorem 3.2], we get a simple characterization
Externí odkaz:
http://arxiv.org/abs/2404.03463
Autor:
Lewark, Lukas
A set L of links is introduced, containing positive braid links as well as arborescent positive Hopf plumbings. It is shown that for links in P, the leading and the second coefficient of the Alexander polynomial have opposite sign. It follows that ce
Externí odkaz:
http://arxiv.org/abs/2402.03155
Autor:
Kalfagianni, Efstratia, Mcconkey, Rob
We use the degree of the colored Jones knot polynomials to show that the crossing number of a $(p,q)$-cable of an adequate knot with crossing number $c$ is larger than $q^2\, c$. As an application we determine the crossing number of $2$-cables of ade
Externí odkaz:
http://arxiv.org/abs/2309.03814
Autor:
Bavier, Brandon, Doleshal, Brandy
We compute the Jones polynomial for a three-parameter family of links, the twisted torus links of the form $T((p,q),(2,s))$ where $p$ and $q$ are coprime and $s$ is nonzero. When $s = 2n$, these links are the twisted torus knots $T(p,q,2,n)$. We show
Externí odkaz:
http://arxiv.org/abs/2308.00502