相关论文: Computing boundary slopes of 2-bridge links
Let $G$ be a connected undirected graph on $n$ vertices with no loops but possibly multiedges. Given an arithmetical structure $(\textbf{r}, \textbf{d})$ on $G$, we describe a construction which associates to it a graph $G'$ on $n-1$…
We introduce a new numerical invariant of knots and links from the descending diagrams. It is considered to live between the unknotting number and the bridge number.
For a hyperbolic knot in $S^3$, Dehn surgery along slope $r \in \Q \cup \{\frac10\}$ is {\em exceptional} if it results in a non-hyperbolic manifold. We say meridional surgery, $r = \frac10$, is {\em trivial} as it recovers the manifold…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
In this paper, we use a partition of the links of a network in order to uncover its community structure. This approach allows for communities to overlap at nodes, so that nodes may be in more than one community. We do this by making a node…
In this paper, we determine a formula for Kemeny's constant for a graph with multiple bridges, in terms of quantities that are inherent to the subgraphs obtained upon removal of all bridges and that can be computed independently. With the…
Computing accurate splines of degree greater than three is still a challenging task in today's applications. In this type of interpolation, high-order derivatives are needed on the given mesh. As these derivatives are rarely known and are…
New presentations of a link and a virtual link are introduced and algebraic systems on links and virtual links are constructed respectively. Based on the algebraic systems, Reduction Crossing Algorithms for them are proposed which are used…
The slope conjecture gives a precise relation between the degree of the colored Jones polynomial of a knot and the boundary slopes of essential surfaces in the knot complement. In this note we propose a generalization of the slope…
We consider the notion of mosaic diagrams for surface-links using marked graph diagrams. We establish bounds, in some cases tight, on the mosaic numbers for the surface-links with ch-index up to 10. As an application, we use mosaic diagrams…
Computing the topology of an algebraic plane curve $\mathcal{C}$ means to compute a combinatorial graph that is isotopic to $\mathcal{C}$ and thus represents its topology in $\mathbb{R}^2$. We prove that, for a polynomial of degree $n$ with…
The fundamental model of any periodic crystal is a periodic set of points at all atomic centres. Since crystal structures are determined in a rigid form, their strongest equivalence is rigid motion (composition of translations and…
In this paper we study the parabolic representations of 2-bridge links by finiding arc coloring vectors on the Conway diagram. The method we use is to convert the system of conjugation quandle equations to that of symplectic quandle…
Let $H(p)$ be the set of 2-bridge knots $K$ whose group $G$ is mapped onto a non-trivial free product, $Z/2 * Z/p$, $p$ being odd. Then there is an algebraic integer $s_0$ such that for any $K$ in $H(p)$, $G$ has a parabolic representation…
We calculate the outerplanar crossing numbers of complete multipartite graphs which have $n$ partite sets with $m$ vertices and one partite set with $p$ vertices, where either $p|mn$ or $mn|p$.
We consider surgery moves along (n+1)-component Brunnian links in compact connected oriented 3-manifolds, where the framing of the each component is 1/k for k in Z. We show that no finite type invariant of degree < 2n-2 can detect such a…
In this paper all two-term tilting complexes over a Brauer tree algebra with multiplicity one are described using a classification of indecomposable two-term partial tilting complexes obtained earlier in a joint paper with M. Antipov. The…
We establish basic information about border rank algorithms for the matrix multiplication tensor and other tensors with symmetry. We prove that border rank algorithms for tensors with symmetry (such as matrix multiplication and the…
We compute, by D-module restrictions, the slopes of irregular hypergeometric systems associated to a monomial curve.
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…