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Pis'ma v Zh. Èksper. Teoret. Fiz., 2015, Volume 101, Issue 12, Pages 931–934 (Mi jetpl4663)  

This article is cited in 18 scientific papers (total in 18 papers)

METHODS OF THEORETICAL PHYSICS

On the defect and stability of differential expansion

Ya. Kononova, A. Morozovbcd

a Higher School of Economics, Math Department, 117312 Moscow, Russia
b Institute for Information Transmission Problems, 127994 Moscow, Russia
c National Research Nuclear University "MEPhI", 15409 Moscow 1, Russia
d Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia

Abstract: Empirical analysis of many colored knot polynomials, made possible by recent computational advances in Chern–Simons theory, reveals their stability: for any given negative $N$ and any given knot the set of coefficients of the polynomial in $r$-th symmetric representation does not change with $r$, if it is large enough. This fact reflects the non-trivial and previously unknown properties of the differential expansion, and it turns out that from this point of view there are universality classes of knots, characterized by a single integer, which we call defect, and which is in fact related to the power of Alexander polynomial.

DOI: https://doi.org/10.7868/S0370274X15120115

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English version:
Journal of Experimental and Theoretical Physics Letters, 2015, 101:12, 831–834

Bibliographic databases:

Document Type: Article
Received: 30.04.2015
Language: English

Citation: Ya. Kononov, A. Morozov, “On the defect and stability of differential expansion”, Pis'ma v Zh. Èksper. Teoret. Fiz., 101:12 (2015), 931–934; JETP Letters, 101:12 (2015), 831–834

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kononov Ya. Morozov A., “Colored Homfly and Generalized Mandelbrot Set”, J. High Energy Phys., 2015, no. 11, 151  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. Yu. Morozov, “Are there $p$-adic knot invariants?”, Theoret. and Math. Phys., 187:1 (2016), 447–454  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Kononov Ya., Morozov A., “On rectangular HOMFLY for twist knots”, Mod. Phys. Lett. A, 31:38 (2016), 1650223  crossref  mathscinet  zmath  isi  elib  scopus
    4. Morozov A., “Differential expansion and rectangular HOMFLY for the figure eight knot”, Nucl. Phys. B, 911 (2016), 582–605  crossref  zmath  isi  elib  scopus
    5. Mironov A., Morozov A., Morozov A., Sleptsov A., “HOMFLY polynomials in representation [3, 1] for 3-strand braids”, J. High Energy Phys., 2016, no. 9, 134  crossref  mathscinet  zmath  isi  scopus
    6. Morozov A., “Factorization of differential expansion for antiparallel double-braid knots”, J. High Energy Phys., 2016, no. 9, 135  crossref  mathscinet  zmath  isi  scopus
    7. Mironov A., Morozov A., Morozov A., Sleptsov A., “Racah matrices and hidden integrability in evolution of knots”, Phys. Lett. B, 760 (2016), 45–58  crossref  isi  elib  scopus
    8. Mironov A. Mkrtchyan R. Morozov A., “On universal knot polynomials”, J. High Energy Phys., 2016, no. 2, 078  crossref  mathscinet  isi  scopus
    9. A. Morozov, Phys. Lett. B, 766 (2017), 291–300  crossref  isi  scopus
    10. A. Yu. Morozov, A. A. Morozov, A. V. Popolitov, “Matrix model and dimensions at hypercube vertices”, Theoret. and Math. Phys., 192:1 (2017), 1039–1079  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. Ya. A. Kononov, A. Yu. Morozov, “Rectangular superpolynomials for the figure-eight knot $4_1$”, Theoret. and Math. Phys., 193:2 (2017), 1630–1646  mathnet  crossref  crossref  adsnasa  isi  elib
    12. A. Mironov, A. Morozov, A. Morozov, P. Ramadevi, V. K. Singh, A. Sleptsov, “Checks of Integrality Properties in Topological Strings”, J. High Energy Phys., 2017, no. 8, 139  crossref  mathscinet  zmath  isi  scopus
    13. Bai C., Jiang J., Liang J., Mironov A., Morozov A., Morozov A., Sleptsov A., “Differential Expansion For Link Polynomials”, Phys. Lett. B, 778 (2018), 197–206  crossref  zmath  isi  scopus
    14. Morozov A., “Homfly For Twist Knots and Exclusive Racah Matrices Inrepresentation [333]”, Phys. Lett. B, 778 (2018), 426–434  crossref  zmath  isi  scopus
    15. Anokhina A. Morozov A., “Are Khovanov-Rozansky Polynomials Consistent With Evolution in the Space of Knots?”, J. High Energy Phys., 2018, no. 4, 066  crossref  mathscinet  isi  scopus
    16. Morozov A., “Knot Polynomials For Twist Satellites”, Phys. Lett. B, 782 (2018), 104–111  crossref  mathscinet  isi  scopus
    17. Morozov A., “Factorization of Differential Expansion For Non-Rectangular Representations”, Mod. Phys. Lett. A, 33:12 (2018), 1850062  crossref  mathscinet  zmath  isi  scopus
    18. Anokhina A., “Towards Formalization of the Soliton Counting Technique For the Khovanov-Rozansky Invariants in the Deformed R-Matrix Approach”, Int. J. Mod. Phys. A, 33:36 (2018), 1850221  crossref  zmath  isi  scopus
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