Related papers: Virtual links are algorithmically recognisable
We construct an algorithm to decide whether two given Legendrian or transverse links are equivalent. In general, the complexity of the algorithm is too high for practical implementation. However, in many cases, when the symmetry group of…
A virtual link is a generalization of a classical link that is defined as an equivalence class of certain diagrams, called virtual link diagrams. It is further generalized to a twisted link. Twisted links are in one-to-one correspondence…
A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative. Normal virtual links have some properties similar to…
A frame is an overcomplete set that can represent vectors(signals) faithfully and stably. Two frames are equivalent if signals can be essentially represented in the same way, which means two frames differ by a permutation, sign change or…
We introduce a new equivalence relation on decorated ribbon graphs, and show that its equivalence classes directly correspond to virtual links. We demonstrate how this correspondence can be used to convert any invariant of virtual links…
In this paper, we establish that the arc shift operation on a $n$-component virtual link diagram acts as an unknotting operation when the virtual link is $n$-homogeneous proper, aiding in the classification of \( n \)-component virtual…
We extend some classical results of Bankwitz, Crowell, and Murasugi to the setting of virtual links. For instance, we show that an alternating virtual link is split if and only if it is visibly split, and that the Alexander polynomial of…
Using a new tool called lassos, we establish a new correspondence between cellular link {diagrams} on closed surfaces and equivalence classes of virtual link {diagrams}. This is analogous to a well-known correspondence among the links…
We study spaces of realisations of linkages (weighted graphs) whose underlying graph is a series parallel graph. In particular, we describe an algorithm for determining whether or not such spaces are connected.
We provide an algorithm to determine whether a link L admits a crossing change that turns it into a split link, under some fairly mild hypotheses on L. The algorithm also provides a complete list of all such crossing changes. It can…
This paper is an introduction to the subject of virtual knot theory, combined with a discussion of some specific new theorems about virtual knots. The new results are as follows: We prove, using a 3-dimensional topology approach that if a…
We give a sufficient condition for an almost alternating link diagram to represent a non-splittable link. The main theorem gives us a way to see if a given almost alternating link diagram represents a splittable link without increasing…
The problem of link prediction, predicting if two nodes in a network have a connection between them, is a theoretical problem with numerous field-agnostic real-world applications. This paper investigates the efficacy of three classes of…
We make use of the complex implicit representation in order to provide a deterministic algorithm for checking whether or not two implicit algebraic curves are related by a similarity, a central question in Pattern Recognition and Computer…
When are two algorithms the same? How can we be sure a recently proposed algorithm is novel, and not a minor twist on an existing method? In this paper, we present a framework for reasoning about equivalence between a broad class of…
In a recent provocative paper, Lamport points out "the insubstantiality of processes" by proving the equivalence of two different decompositions of the same intuitive algorithm by means of temporal formulas. We point out that the correct…
When are two algorithms the same? How can we be sure a recently proposed algorithm is novel, and not a minor variation on an existing method? In this paper, we present a framework for reasoning about equivalence between a broad class of…
If L_1 and L_2 are two Brunnian links with all pairwise linking numbers 0, then we show that L_1 and L_2 are equivalent if and only if they have homeomorphic complements. In particular, this holds for all Brunnian links with at least three…
A virtual link may be defined as an equivalence class of diagrams, or alternatively as a stable equivalence class of links in thickened surfaces. We prove that a minimal crossing virtual link diagram has minimal genus across representatives…
The virtual genus of a virtual satellite link is equal to that of its companion.