A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Formula found for a specific knot's A-polynomial.
We construct an integer polynomial whose coefficients enumerate the Kauffman states of the two-bridge knot with Conway's notation C(n,r).
An explicit formula for the -polynomial of the knot with Conway's notation is obtained from the explicit Riley-Mednykh polynomial of it.
We calculate the Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation using the Schläfli formula for the generalized Chern-Simons function on the family of cone-manifold structures. We present the concrete and explicit formula of them. We apply the general instruct…
This article contains general formulas for Tutte and Jones polynomial for families of knots and links given in Conway notation.
For families of knots and links given in Conway notation we compute lower maximal and upper minimal bound of hyperbolic volume by using source links and augmented links.
This article contains general formulas for Tutte and Jones polynomials for families of knots and links given in Conway notation and "portraits of families"-- plots of zeroes of their corresponding Jones polynomials.
After defining reduced minimum braid word and criteria for a braid family representative, different braid family representatives are derived, and a correspondence between them and families of knots and links given in Conway notation is established.
This paper contains general formulae for the reduced relative Tutte, Kauffman bracket and Jones polynomials of families of virtual knots and links given in Conway notation and discussion of a counterexample to the Z-move conjecture of Fenn, Kauffman and Manturov.
We give explicit formulae for the volumes of hyperbolic cone-manifolds of double twist knots, a class of two-bridge knots which includes twist knots and two-bridge knots with Conway notation . We also study the Riley polynomial of a class of one-relator groups which includes two-bridge knot groups.
In this paper, we discuss the region unknotting number of different classes of 2-bridge knots. In particular, we provide region unknotting number for the classes of -bridge knots whose Conway notation is and . By generalizing, we also provide a sharp up…
We extend some part of the unpublished paper written by Mednykh and Rasskazov. Using the approach indicated in this paper we derive the Riley-Mednykh polynomial for some family of the -bridge knot orbifolds. As a result we obtain explicit formulae for the volume of cone-manifolds and the Chern-Simons invariant of or…
For a knot K in S^3, let T(K) be the characteristic toric sub-orbifold of the orbifold (S^3,K) as defined by Bonahon and Siebenmann. If K has unknotting number one, we show that an unknotting arc for K can always be found which is disjoint from T(K), unless either K is an EM-knot (of Eudave-Munoz) or (S^3,K) contains a…
Study on left orderability of specific knot covers.
New -manifolds without - and -handles are created from knots.
Pseudodiagrams are diagrams of knots where some information about which strand goes over/under at certain crossings may be missing. Pseudoknots are equivalence classes of pseudodiagrams, with equivalence defined by a class of Reidemeister-type moves. In this paper, we introduce two natural extensions of classical knot …
Let be the family of two bridge knots of slope . We calculate the volumes of the cone-manifolds using the Schläfli formula. We present the concrete and explicit formula of them. We apply the general instructions of Hilden, Lozano, and Montesinos-Amilibia and extend the Ham, Mednykh,…
The paper finds left orderable slopes for specific double twist knots.
We present computational results about quasi-alternating knots and links and odd homology obtained by looking at link families in the Conway notation. More precisely, we list quasi-alternating links up to 12 crossings and the first examples of quasi-alternating knots and links with at least two different minimal diagra…
Proposes a new notation for biracks to simplify rack structure analysis.
Graphical notation simplifies tensor operations and decompositions.
Unified notation simplifies information-theoretic concepts in machine learning.
In~\cite{Kim} the author generalized the Conway algebra and constructed the invariant valued in the generalized Conway algebra defined by applying two skein relations to crossings, which is called a generalized Conway type invariant. The generalized Conway type invariant is a generalization of Homflypt polynomial. In t…
A simplified proof of the Alexander-Conway polynomial exists.
Graphical notation simplifies complex polynomial constraints in linear models.
We consider an algebra of (classical or virtual) tangles over an ordered circuit operad and introduce Conway-type invariants of tangles which respect this algebraic structure. The resulting invariants contain both the coefficients of the Conway polynomial and the Milnor's mu-invariants of string links as partial cases.…
L-space knots lack essential Conway spheres, proven with Floer theory.
The paper characterizes Conway-Coxeter friezes using rational links.
In the present paper, we build a bridge between Conway-Coxeter friezes and rational tangles through the Kauffman bracket polynomials. One can compute a Kauffman bracket polynomials attached to rational links by using Conway-Coxeter friezes. As an application one can give a complete invariant on Conway-Coxeter friezes o…
We give a closed formula for the Conway function of a splice in terms of the Conway function of its splice components. As corollaries, we refine and generalize results of Seifert, Torres, and Sumners-Woods.
The Conway knot can't be smoothly tied to any other knot an infinite number of times.
We give a geometric construction of the multivariable Conway potential function for colored links. In the case of a single color, it is Kauffman's definition of the Conway polynomial in terms of a Seifert matrix.
The Conway potential function (CPF) for colored links is a convenient version of the multi-variable Alexander-Conway polynomial. We give a skein characterization of CPF, much simpler than the one by Murakami. In particular, Conway's `smoothing of crossings' is not in the axioms. The proof uses a reduction scheme in a t…
Paper simplifies concentration inequalities for easier probabilistic analysis.
We obtain bounds on hyperbolic volume for periodic links and Conway sums of alternating tangles. For links that are Conway sums we also bound the hyperbolic volume in terms of the coefficients of the Jones polynomial.
Khovanov homology invariant under Conway mutation.
Lisa Piccirillo solved the mystery of the Conway knot's sliceness.
In this chapter (Chapter III) we introduce the concept of Conway algebras (the notion related to entropic magmas) and describe invariants of links yielded by (partial) Conway algebras (including the Homflypt polynomial and signatures). We present, in detail, a proof (following the original Przytycki-Traczyk 1984 proof)…
Families of alternating knots (links) and tangles are studied using as building block the conway defined as the twisting of two strands. The regular representation of knots assumes the projection has the minimal number of overpassings, and the minimal number of conways. The continued fraction associated to rational kno…
Paper defines half-Conway polynomial and computes it for knots up to 12 crossings.
Two knot families meet cosmetic surgery conjecture.
Extends Benard-Conway invariant to all two-component links.
Simplified proof for a theorem about graphs.
Study proves nontrivial knots can't undergo cosmetic surgeries.
In 1983, Conway and Gordon proved that for every spatial complete graph on six vertices, the sum of the linking numbers over all of the constituent two-component links is odd, and that for every spatial complete graph on seven vertices, the sum of the Arf invariants over all of the Hamiltonian knots is odd. In 2009, th…
Improved math problem solvers using Transformer networks and diverse notations.
We give a counterexample to the Kawauchi conjecture on the Conway polynomial of achiral knots which asserts that the Conway polynomial of an achiral knot satisfies the splitting property for a polynomial with integer coefficients. We show that the Bonahon-Siebenmann decomposition of an ac…
New theorem shows every integer can be represented by knot summation.