Log in

Relevant bibliographies by topics / Homfly / Journal articles

To see the other types of publications on this topic, follow the link: Homfly.

Journal articles on the topic 'Homfly'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Homfly.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Zhu, Shengmao. "A simple proof of the strong integrality for full colored HOMFLYPT invariants." Journal of Knot Theory and Its Ramifications 28, no. 07 (June 2019): 1950046. http://dx.doi.org/10.1142/s0218216519500469.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

MORTON, H. R. "Mutant knots with symmetry." Mathematical Proceedings of the Cambridge Philosophical Society 146, no. 1 (January 2009): 95–107. http://dx.doi.org/10.1017/s0305004108001862.

Full text

Abstract:

AbstractMutant knots, in the sense of Conway, are known to share the same Homfly polynomial. Their 2-string satellites also share the same Homfly polynomial, but in general theirm-string satellites can have different Homfly polynomials form> 2. We show that, under conditions of extra symmetry on the constituent 2-tangles, the directedm-string satellites of mutants share the same Homfly polynomial form< 6 in general, and for all choices ofmwhen the satellite is based on a cable knot pattern.We give examples of mutants with extra symmetry whose Homfly polynomials of some 6-string satellites are different, by comparing their quantumsl(3) invariants.

APA, Harvard, Vancouver, ISO, and other styles

3

LAVROV, MIKHAIL, and DAN RUTHERFORD. "ON THE S1 × S2 HOMFLY-PT INVARIANT AND LEGENDRIAN LINKS." Journal of Knot Theory and Its Ramifications 22, no. 08 (July 2013): 1350040. http://dx.doi.org/10.1142/s0218216513500405.

Full text

Abstract:

In [On the HOMFLY-PT skein module of S1 × S2, Math. Z. 237(4) (2001) 769–814], Gilmer and Zhong established the existence of an invariant for links in S1 × S2 which is a rational function in variables a and s and satisfies the HOMFLY-PT skein relations. We give formulas for evaluating this invariant in terms of a standard, geometrically simple basis for the HOMFLY-PT skein module of the solid torus. This allows computation of the invariant for arbitrary links in S1 × S2 and shows that the invariant is in fact a Laurent polynomial in a and z = s – s-1. Our proof uses connections between HOMFLY-PT skein modules and invariants of Legendrian links. As a corollary, we extend HOMFLY-PT polynomial estimates for the Thurston–Bennequin number to Legendrian links in S1 × S2 with its tight contact structure.

APA, Harvard, Vancouver, ISO, and other styles

4

MORTON, H. R., and N. D. A. RYDER. "Relations between Kauffman and Homfly satellite invariants." Mathematical Proceedings of the Cambridge Philosophical Society 149, no. 1 (March 16, 2010): 105–14. http://dx.doi.org/10.1017/s0305004110000058.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Kawagoe, Kenichi. "On the skeins in the annulus and applications to invariants of 3-manifolds." Journal of Knot Theory and Its Ramifications 07, no. 02 (March 1998): 187–203. http://dx.doi.org/10.1142/s0218216598000127.

Full text

Abstract:

In this paper, we relate Schur functions and a linear skein of annulus derived from the Homfly polynomail. Using this relations, we define topological invariants of 3-manifolds from the Homfly polynomial.

APA, Harvard, Vancouver, ISO, and other styles

6

Dowlin, Nathan. "The knot Floer cube of resolutions and the composition product." Journal of Knot Theory and Its Ramifications 29, no. 03 (March 2020): 2050006. http://dx.doi.org/10.1142/s0218216520500066.

Full text

Abstract:

We examine the relationship between the oriented cube of resolutions for knot Floer homology and HOMFLY-PT homology. By using a filtration induced by additional basepoints on the Heegaard diagram for a knot [Formula: see text], we see that the filtered complex decomposes as a direct sum of HOMFLY-PT complexes of various subdiagrams. Applying Jaeger’s composition product formula for knot polynomials, we deduce that the graded Euler characteristic of this direct sum is the HOMFLY-PT polynomial of [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

7

Altun, Y. "On the Homfly polynomial." International Mathematical Forum 2 (2007): 2753–57. http://dx.doi.org/10.12988/imf.2007.07247.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

CHAN, TAT-HUNG. "POLYNOMIALS FOR A FAMILY OF BRUNNIAN LINKS." Journal of Knot Theory and Its Ramifications 09, no. 05 (August 2000): 587–609. http://dx.doi.org/10.1142/s0218216500000335.

Full text

Abstract:

We apply skein relations to derive recurrence relations for the HOMFLY polynomials of a family of Brunnian links. Solution of the recurrence relations yields closed-form formulas for the HOMFLY and hence the Jones polynomials.

APA, Harvard, Vancouver, ISO, and other styles

9

KAUFFMAN, LOUIS H., and PIERRE VOGEL. "LINK POLYNOMIALS AND A GRAPHICAL CALCULUS." Journal of Knot Theory and Its Ramifications 01, no. 01 (March 1992): 59–104. http://dx.doi.org/10.1142/s0218216592000069.

Full text

Abstract:

This paper constructs invariants of rigid vertex isotopy for graphs embedded in three dimensional space. For the Homfly and Dubrovnik polynomials, the skein formalism for these invariants is as shown below. Homfly. [Formula: see text] Dubrovnik. [Formula: see text]

APA, Harvard, Vancouver, ISO, and other styles

10

KIM, JAEHOO PARK. "A HOMFLY-PT POLYNOMIAL OF LINKS IN A SOLID TORUS." Journal of Knot Theory and Its Ramifications 08, no. 06 (September 1999): 709–20. http://dx.doi.org/10.1142/s0218216599000456.

Full text

Abstract:

In this paper a Homfly-pt type Laurant polynomial1 for links in S1 × D2 is defined. This invariant is defined by giving an algebra and a trace, analogous to the Hecke algebra construction of the Homfly-pt polynomial for links in S3.

APA, Harvard, Vancouver, ISO, and other styles

11

MORTON, H. R., and N. RYDER. "INVARIANTS OF GENUS 2 MUTANTS." Journal of Knot Theory and Its Ramifications 18, no. 10 (October 2009): 1423–38. http://dx.doi.org/10.1142/s0218216509007506.

Full text

Abstract:

Pairs of genus 2 mutant knots can have different Homfly polynomials, for example some 3-string satellites of Conway mutant pairs. We give examples which have different Kauffman 2-variable polynomials, answering a question raised by Dunfield et al. in their study of genus 2 mutants. While pairs of genus 2 mutant knots have the same Jones polynomial, given from the Homfly polynomial by setting v = s2, we give examples whose Homfly polynomials differ when v = s3. We also give examples which differ in a Vassiliev invariant of degree 7, in contrast to satellites of Conway mutant knots.

APA, Harvard, Vancouver, ISO, and other styles

12

NAKABO, SHIGEKAZU. "EXPLICIT DESCRIPTION OF THE HOMFLY POLYNOMIALS FOR 2-BRIDGE KNOTS AND LINKS." Journal of Knot Theory and Its Ramifications 11, no. 04 (June 2002): 565–74. http://dx.doi.org/10.1142/s0218216502001834.

Full text

Abstract:

An explicit formula of the HOMFLY polynomial of 2-bridge knots and links is presented. As corollaries, some specific coefficient polynomials are described explicitly. Lastly, some examples are calculated, which are related to the classification problem of the 2-bridge knots and links by the HOMFLY polynomial.

APA, Harvard, Vancouver, ISO, and other styles

13

Nawata, Satoshi, P. Ramadevi, and Vivek Kumar Singh. "Colored HOMFLY-PT polynomials that distinguish mutant knots." Journal of Knot Theory and Its Ramifications 26, no. 14 (December 2017): 1750096. http://dx.doi.org/10.1142/s0218216517500961.

Full text

Abstract:

We illustrate from the viewpoint of braiding operations on WZNW conformal blocks how colored HOMFLY-PT polynomials with multiplicity structure can detect mutations. As an example, we explicitly evaluate the [Formula: see text]-colored HOMFLY-PT polynomials that distinguish a famous mutant pair, Kinoshita–Terasaka and Conway knot.

APA, Harvard, Vancouver, ISO, and other styles

14

NAWATA, SATOSHI, P. RAMADEVI, and ZODINMAWIA. "COLORED HOMFLY POLYNOMIALS FROM CHERN–SIMONS THEORY." Journal of Knot Theory and Its Ramifications 22, no. 13 (November 2013): 1350078. http://dx.doi.org/10.1142/s0218216513500788.

Full text

Abstract:

We elaborate the Chern–Simons field theoretic method to obtain colored HOMFLY invariants of knots and links. Using multiplicity-free quantum 6j-symbols for Uq(𝔰𝔩N), we present explicit evaluations of the HOMFLY invariants colored by symmetric representations for a variety of knots, two-component links and three-component links.

APA, Harvard, Vancouver, ISO, and other styles

15

CHAN, TAT-HUNG. "HOMFLY POLYNOMIALS OF ITERATIVE FAMILIES OF LINKS." Journal of Knot Theory and Its Ramifications 11, no. 01 (February 2002): 1–12. http://dx.doi.org/10.1142/s0218216502001469.

Full text

Abstract:

We show that if a family of oriented links obey an iterative pattern, their HOMFLY polynomials satisfy a homogeneous linear recurrence relation. The construction embodied in the proof is applied to derive explicit formulas for the HOMFLY polynomials of some iterative families, including the torus links {Tn,3}n≥0.

APA, Harvard, Vancouver, ISO, and other styles

16

Jin, Xian’an, and Fuji Zhang. "The Homfly and dichromatic polynomials." Proceedings of the American Mathematical Society 140, no. 4 (April 1, 2012): 1459–72. http://dx.doi.org/10.1090/s0002-9939-2011-11050-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Hsieh, Chun-Chung. "A non-HOMFLY knot invariant." Journal of Geometry and Physics 131 (September 2018): 101–13. http://dx.doi.org/10.1016/j.geomphys.2018.05.006.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Mironov, A. D., A. Yu Morozov, and A. V. Sleptsov. "Genus expansion of HOMFLY polynomials." Theoretical and Mathematical Physics 177, no. 2 (November 2013): 1435–70. http://dx.doi.org/10.1007/s11232-013-0115-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Tao, Zhi-Xiong. "Some new examples of links with the same polynomials." Journal of Knot Theory and Its Ramifications 29, no. 07 (June 2020): 2050049. http://dx.doi.org/10.1142/s0218216520500492.

Full text

Abstract:

We call a link (knot) [Formula: see text] to be strongly Jones (respectively, Homfly) undetectable, if there are infinitely many links which are not isotopic to [Formula: see text] but share the same Jones (respectively, Homfly) polynomial as [Formula: see text]. We reconstruct Kanenobu’s knot [Kanenobu, Infinitely many knots with the same polynomial invariant, Proc. Amer. Math. Soc. 97(1) (1986), 158–162] and give two new constructions. Using these constructions, we give some examples of strongly Jones undetectable: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] ([Formula: see text] is the mirror image of [Formula: see text]) and etc. For some special cases, these constructions will be shown to be strongly Jones undetectable and strongly Homfly undetectable.

APA, Harvard, Vancouver, ISO, and other styles

20

MORTON, HUGH R., and SASCHA G. LUKAC. "THE HOMFLY POLYNOMIAL OF THE DECORATED HOPF LINK." Journal of Knot Theory and Its Ramifications 12, no. 03 (May 2003): 395–416. http://dx.doi.org/10.1142/s0218216503002536.

Full text

Abstract:

The main goal is to find the Homfly polynomial of a link formed by decorating each component of the Hopf link with the closure of a directly oriented tangle. Such decorations are spanned in the Homfly skein of the annulus by elements Qλ, depending on partitions λ. We show how the 2-variable Homfly invariant <λ, μ> of the Hopf link arising from decorations Qλ and Qμ can be found from the Schur symmetric function sμ of an explicit power series depending on λ. We show also that the quantum invariant of the Hopf link coloured by irreducible sl(N)q modules Vλ and Vμ, which is a 1-variable specialisation of <λ, μ>, can be expressed in terms of an N × N minor of the Vandermonde matrix (qij).

APA, Harvard, Vancouver, ISO, and other styles

21

Kato, Keiju. "Interior polynomial for signed bipartite graphs and the HOMFLY polynomial." Journal of Knot Theory and Its Ramifications 29, no. 12 (October 2020): 2050077. http://dx.doi.org/10.1142/s0218216520500777.

Full text

Abstract:

The interior polynomial is a Tutte-type invariant of bipartite graphs, and a part of the HOMFLY polynomial of a special alternating link coincides with the interior polynomial of the Seifert graph of the link. We extend the interior polynomial to signed bipartite graphs, and we show that, in the planar case, it is equal to the maximal [Formula: see text]-degree part of the HOMFLY polynomial of a naturally associated link. Note that the latter can be any oriented link. This result fits into a program aimed at deriving the HOMFLY polynomial from Floer homology. We also establish some other, more basic properties of the signed interior polynomial. For example, the HOMFLY polynomial of the mirror image of [Formula: see text] is given by [Formula: see text]. This implies a mirroring formula for the signed interior polynomial in the planar case. We prove that the same property holds for any bipartite graph and the same graph with all signs reversed. The proof relies on Ehrhart reciprocity applied to the so-called root polytope. We also establish formulas for the signed interior polynomial inspired by the knot theoretical notions of flyping and mutation. This leads to new identities for the original unsigned interior polynomial.

APA, Harvard, Vancouver, ISO, and other styles

22

衣, 鹏宇. "The HOMFLY Polynomials of Class of Links." Advances in Applied Mathematics 10, no. 08 (2021): 2794–802. http://dx.doi.org/10.12677/aam.2021.108291.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

CHAN, TAT-HUNG. "HOMFLY Polynomials of Some Generalized Hopf Links." Journal of Knot Theory and Its Ramifications 09, no. 07 (November 2000): 865–83. http://dx.doi.org/10.1142/s0218216500000499.

Full text

Abstract:

The Hopf link, consisting of two unknots wrapped around each other, is the simplest possible nontrivial link with more than one component. We can generalize it to two bundles of "parallel" unknots wrapped around each other. In this paper, we show that when one of the two bundles has a fixed side, the HOMFLY polynomials of the links satisfy a system of recurrence equations. This leads to a procedure for computing explicit formulas for the HOMFLY polynomials.

APA, Harvard, Vancouver, ISO, and other styles

24

Sleptsov, Alexey. "Hidden structures of knot invariants." International Journal of Modern Physics A 29, no. 29 (November 20, 2014): 1430063. http://dx.doi.org/10.1142/s0217751x14300634.

Full text

Abstract:

We discuss a connection of HOMFLY polynomials with Hurwitz covers and represent a generating function for the HOMFLY polynomial of a given knot in all representations as Hurwitz partition function, i.e. the dependence of the HOMFLY polynomials on representation R is naturally captured by symmetric group characters (cut-and-join eigenvalues). The genus expansion and the loop expansion through Vassiliev invariants explicitly demonstrate this phenomenon. We study the genus expansion and discuss its properties. We also consider the loop expansion in details. In particular, we give an algorithm to calculate Vassiliev invariants, give some examples and discuss relations among Vassiliev invariants. Then we consider superpolynomials for torus knots defined via double affine Hecke algebra. We claim that the superpolynomials are not functions of Hurwitz type: symmetric group characters do not provide an adequate linear basis for their expansions. Deformation to superpolynomials is, however, straightforward in the multiplicative basis: the Casimir operators are beta-deformed to Hamiltonians of the Calogero–Moser–Sutherland system. Applying this trick to the genus and Vassiliev expansions, we observe that the deformation is fully straightforward only for the thin knots. Beyond the family of thin knots additional algebraically independent terms appear in the Vassiliev expansions. This can suggest that the superpolynomials do in fact contain more information about knots than the colored HOMFLY and Kauffman polynomials.

APA, Harvard, Vancouver, ISO, and other styles

25

Kanenobu, Taizo, and Yasuyuki Miyazawa. "Homfly polynomials as vassiliev link invariants." Banach Center Publications 42, no. 1 (1998): 165–85. http://dx.doi.org/10.4064/-42-1-165-185.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Morton, Hugh R., and Richard J. Hadji. "Homfly polynomials of generalized Hopf links." Algebraic & Geometric Topology 2, no. 1 (January 15, 2002): 11–32. http://dx.doi.org/10.2140/agt.2002.2.11.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Morton, H. R. "Integrality of Homfly 1–tangle invariants." Algebraic & Geometric Topology 7, no. 1 (March 29, 2007): 327–38. http://dx.doi.org/10.2140/agt.2007.7.327.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Krasner, Daniel. "Integral HOMFLY-PT and -Link Homology." International Journal of Mathematics and Mathematical Sciences 2010 (2010): 1–25. http://dx.doi.org/10.1155/2010/896879.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Kononov, Ya, and A. Morozov. "On rectangular HOMFLY for twist knots." Modern Physics Letters A 31, no. 38 (November 25, 2016): 1650223. http://dx.doi.org/10.1142/s0217732316502230.

Full text

Abstract:

As a new step in the study of rectangularly-colored knot polynomials, we reformulate the prescription [A. Morozov, arXiv:1606.06015v8 ] for twist knots in the double-column representations [Formula: see text] in terms of skew Schur polynomials. These, however, are mysteriously shifted from the standard topological locus, which makes further generalization to arbitrary [Formula: see text] not quite straightforward.

APA, Harvard, Vancouver, ISO, and other styles

30

GANZELL, SANDY, and AMY V. KAPP. "CHIRALITY VS. HOMFLY AND KAUFFMAN POLYNOMIALS." Journal of Knot Theory and Its Ramifications 17, no. 12 (December 2008): 1519–24. http://dx.doi.org/10.1142/s0218216508006725.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Maulik, Davesh. "Stable pairs and the HOMFLY polynomial." Inventiones mathematicae 204, no. 3 (November 30, 2015): 787–831. http://dx.doi.org/10.1007/s00222-015-0624-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Lickorish, W. B. R. "Sampling the SU(N) Invariants of Three-Manifolds." Journal of Knot Theory and Its Ramifications 06, no. 01 (February 1997): 45–60. http://dx.doi.org/10.1142/s0218216597000054.

Full text

Abstract:

The SU(N) quantum invariants for three-manifolds have been established in a combinatorial way by Yokota starting from the skein theory associated with the HOMFLY polynomial invariant of knot theory. Using Yokota's formulation it is here noted that there are distinct three-manifolds that are not distinguished by these invariants and that there are manifolds distinguished by the SU(N) invariants for N ≥ 3 that have the same SU(2) invariants. A by-product of the investigation is a reversing result for the HOMFLY polynomial.

APA, Harvard, Vancouver, ISO, and other styles

33

PARIS, LUIS, and EMMANUEL WAGNER. "HOMFLY-PT SKEIN MODULE OF SINGULAR LINKS IN THE THREE-SPHERE." Journal of Knot Theory and Its Ramifications 22, no. 02 (February 2013): 1350005. http://dx.doi.org/10.1142/s0218216513500053.

Full text

Abstract:

For a ring R, we denote by [Formula: see text] the free R-module spanned by the isotopy classes of singular links in 𝕊3. Given two invertible elements x, t ∈ R, the HOMFLY-PT skein module of singular links in 𝕊3 (relative to the triple (R, t, x)) is the quotient of [Formula: see text] by local relations, called skein relations, that involve t and x. We compute the HOMFLY-PT skein module of singular links for any R such that (t-1 - t + x) and (t-1 - t - x) are invertible. In particular, we deduce the Conway skein module of singular links.

APA, Harvard, Vancouver, ISO, and other styles

34

MORTON, HUGH R., and PETER R. CROMWELL. "DISTINGUISHING MUTANTS BY KNOT POLYNOMIALS." Journal of Knot Theory and Its Ramifications 05, no. 02 (April 1996): 225–38. http://dx.doi.org/10.1142/s0218216596000163.

Full text

Abstract:

We consider the problem of distinguishing mutant knots using invariants of their satellites. We show, by explicit calculation, that the Homfly polynomial of the 3-parallel (and hence the related quantum invariants) will distinguish some mutant pairs. Having established a condition on the colouring module which forces a quantum invariant to agree on mutants, we explain several features of the difference between the Homfly polynomials of satellites constructed from mutants using more general patterns. We illustrate this by our calculations; from these we isolate some simple quantum invariants, and a framed Vassiliev invariant of type 11, which distinguish certain mutants, including the Conway and Kinoshita-Teresaka pair.

APA, Harvard, Vancouver, ISO, and other styles

35

Stoimenow, A. "On Cabled Knots and Vassiliev Invariants (Not) Contained in Knot Polynomials." Canadian Journal of Mathematics 59, no. 2 (April 1, 2007): 418–48. http://dx.doi.org/10.4153/cjm-2007-018-0.

Full text

Abstract:

AbstractIt is known that the Brandt–Lickorish–Millett–Ho polynomial Q contains Casson's knot invariant. Whether there are (essentially) other Vassiliev knot invariants obtainable from Q is an open problem. We show that this is not so up to degree 9. We also give the (apparently) first examples of knots not distinguished by 2-cable HOMFLY polynomials which are not mutants. Our calculations provide evidence of a negative answer to the question whether Vassiliev knot invariants of degree d ≤ 10 are determined by the HOMFLY and Kauffman polynomials and their 2-cables, and for the existence of algebras of such Vassiliev invariants not isomorphic to the algebras of their weight systems.

APA, Harvard, Vancouver, ISO, and other styles

36

Zhou, Xin, and Shengmao Zhu. "A new approach to Lickorish–Millett type formulae." Journal of Knot Theory and Its Ramifications 26, no. 13 (November 2017): 1750086. http://dx.doi.org/10.1142/s0218216517500869.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Bigelow, Stephen. "A homological definition of the HOMFLY polynomial." Algebraic & Geometric Topology 7, no. 3 (October 15, 2007): 1409–40. http://dx.doi.org/10.2140/agt.2007.7.1409.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Qazaqzeh, K., A. Aboufattoum, E. Elsakhawy, and A. Diab. "Homfly Polynomial of Knotted Trivalent Plane Graphs." Asian Research Journal of Mathematics 7, no. 2 (January 10, 2017): 1–7. http://dx.doi.org/10.9734/arjom/2017/37847.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Jaeger, François. "A Combinatorial Model for the Homfly Polynomial." European Journal of Combinatorics 11, no. 6 (November 1990): 549–57. http://dx.doi.org/10.1016/s0195-6698(13)80040-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Mackaay, Marco, Marko Stošić, and Pedro Vaz. "The 1,2-coloured HOMFLY-PT link homology." Transactions of the American Mathematical Society 363, no. 04 (April 1, 2011): 2091. http://dx.doi.org/10.1090/s0002-9947-2010-05155-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Chen, Qingtao, and Nicolai Reshetikhin. "Recursion formulas for HOMFLY and Kauffman invariants." Journal of Knot Theory and Its Ramifications 23, no. 05 (April 2014): 1450024. http://dx.doi.org/10.1142/s0218216514500242.

Full text

Abstract:

In this paper, we describe the recursion relations between two parameter HOMFLY and Kauffman polynomials of framed links. These relations correspond to embeddings of quantized universal enveloping algebras. The relation corresponding to embeddings gn ⊃ gk × sln-k where gn is either so2n+1, so2n or sp2n is new.

APA, Harvard, Vancouver, ISO, and other styles

42

Alexandrov, A., A. Mironov, A. Morozov, and And Morozov. "Towards matrix model representation of HOMFLY polynomials." JETP Letters 100, no. 4 (October 2014): 271–78. http://dx.doi.org/10.1134/s0021364014160036.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Mironov, Andrei, Alexei Morozov, and Andrey Morozov. "On colored HOMFLY polynomials for twist knots." Modern Physics Letters A 29, no. 34 (November 6, 2014): 1450183. http://dx.doi.org/10.1142/s0217732314501831.

Full text

Abstract:

Recent results of Gu and Jockers provide the lacking initial conditions for the evolution method in the case of the first nontrivially colored HOMFLY polynomials H[21] for the family of twist knots. We describe this application of the evolution method, which finally allows one to penetrate through the wall between (anti)symmetric and non-rectangular representations for a whole family. We reveal the necessary deformation of the differential expansion, what, together with the recently suggested matrix model approach gives new opportunities to guess what it could be for a generic representation, at least for the family of twist knots.

APA, Harvard, Vancouver, ISO, and other styles

44

Wedrich, Paul. "Exponential growth of colored HOMFLY-PT homology." Advances in Mathematics 353 (September 2019): 471–525. http://dx.doi.org/10.1016/j.aim.2019.06.023.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Liu, Shuya, and Heping Zhang. "The HOMFLY polynomials of odd polyhedral links." Journal of Mathematical Chemistry 51, no. 5 (February 19, 2013): 1310–28. http://dx.doi.org/10.1007/s10910-013-0147-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Cheng, Xiao-Sheng, Yujuan Lei, and Weiling Yang. "The Homfly polynomial of double crossover links." Journal of Mathematical Chemistry 52, no. 1 (July 28, 2013): 23–41. http://dx.doi.org/10.1007/s10910-013-0241-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Anokhina, A. S., and A. A. Morozov. "Cabling procedure for the colored HOMFLY polynomials." Theoretical and Mathematical Physics 178, no. 1 (February 2014): 1–58. http://dx.doi.org/10.1007/s11232-014-0129-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

ANDERSEN, JØRGEN ELLEGAARD, and VLADIMIR TURAEV. "HIGHER SKEIN MODULES." Journal of Knot Theory and Its Ramifications 08, no. 08 (December 1999): 963–84. http://dx.doi.org/10.1142/s0218216599000626.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

ITOYAMA, H., A. MIRONOV, A. MOROZOV, and AND MOROZOV. "EIGENVALUE HYPOTHESIS FOR RACAH MATRICES AND HOMFLY POLYNOMIALS FOR 3-STRAND KNOTS IN ANY SYMMETRIC AND ANTISYMMETRIC REPRESENTATIONS." International Journal of Modern Physics A 28, no. 03n04 (February 10, 2013): 1340009. http://dx.doi.org/10.1142/s0217751x13400095.

Full text

Abstract:

Character expansion expresses extended HOMFLY polynomials through traces of products of finite-dimensional [Formula: see text]- and Racah mixing matrices. We conjecture that the mixing matrices are expressed entirely in terms of the eigenvalues of the corresponding [Formula: see text]-matrices. Even a weaker (and, perhaps, more reliable) version of this conjecture is sufficient to explicitly calculate HOMFLY polynomials for all the 3-strand braids in arbitrary (anti)symmetric representations. We list the examples of so obtained polynomials for R = [3] and R = [4], and they are in accordance with the known answers for torus and figure-eight knots, as well as for the colored special and Jones polynomials. This provides an indirect evidence in support of our conjecture.

APA, Harvard, Vancouver, ISO, and other styles

50

Jordan, S. P., and P. Wocjan. "Estimating Jones and HOMFLY polynomials with one clean qubit." Quantum Information and Computation 9, no. 3&4 (March 2009): 264–89. http://dx.doi.org/10.26421/qic9.3-4-6.

Full text

Abstract:

The Jones and HOMFLY polynomials are link invariants with close connections to quantum computing. It was recently shown that finding a certain approximation to the Jones polynomial of the trace closure of a braid at the fifth root of unity is a complete problem for the one clean qubit complexity class\cite{Shor_Jordan}. This is the class of problems solvable in polynomial time on a quantum computer acting on an initial state in which one qubit is pure and the rest are maximally mixed. Here we generalize this result by showing that one clean qubit computers can efficiently approximate the Jones and single-variable HOMFLY polynomials of the trace closure of a braid at \emph{any} root of unity.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!