LIST OF PUBLICATIONS

Sergei V. Chmutov

PUBLISHED BOOKS.

1. S.V.Chmutov, S.Duzhin, J.Mostovoy, Introduction to Vassiliev Knot Invariants.
Cambridge University Press (2012) ISBN 978-1-107-02083-2. (504 pages). Preprint arXiv:1103.5628v2 [math.GT].

PUBLISHED PAPAERS.

1. S.V.Chmutov, Monodromy groups of critical points of functions in two variables, Funk. anal. 15 No.1 (1981) 61-66. (in Russian).

(English translation: Functional Analysis and its applications. 15 (1981) 48-52)

2. S.V.Chmutov, Monodromy groups of critical points of functions, Invent. math. 67 (1982) 123-131.

3. S.V.Chmutov, Monodromy groups of critical points of functions.II, Invent. math. 73 (1983) 491-510.

4. S.V.Chmutov, Spectrum and equivariant deformations of critical points, Uspehi mat. nauk 39 No.4 (1984) 113-114. (in Russian).

5. S.V.Chmutov, A.N.Varchenko, Finite groups generated by reflections are monodromy groups for some singularities, Funk. anal. 18 No.3 (1984) 1-13. (in Russian).

(English translation: Functional Analysis and its applications. 18 (1984) 171-183)

6. S.V.Chmutov, A.N.Varchenko, On the tangent cone to stratum µ = const, Vestnik MGU, Ser. math. No.1 (1985) 6-9. (in Russian).

(English translation: Moscow University Mathematics Bulletin, No.1 (1985) 5-8)

7. S.V.Chmutov, E.A.Gaydar, I.M.Ignatovich, V.F.Kozadoy, A.P.Nemytykh, V.A.Pinchuk, Implementation of the symbol analytic transformation language FLAC, Proceedings DISCO'90, Lecture Notes in Computer Science 429 (1990) 276-277.

8. S.V.Chmutov, Projective surfaces with a large number of singularities, Singularity conference, IRMA (1991) 10-11.

9. S.V.Chmutov, Extremal distributions of critical points and critical values, In Singularity Theory Trieste (1991). Editors: D.T.Le, K.Saito and B.Teissier. World Sci. Publishing, River Edge, NJ, 1995, 192-205.

10. S.V.Chmutov, I.M.Ignatovich, T.G. Tonchev, The programming language for geometrical constructions with compasses and ruler, Proceedings of the second international conference "New computer technologies in education", Troitsk (1991) 55-56.

11. S.V.Chmutov, Examples of projective surfaces with many singularities, Journal of Algebraic Geometry 1 (1992) 191-196.

12. S.V.Chmutov, Two properties of Gröbner bases, Programmirovanie 5 (1992) 70-72. (in Russian)

(English translation: Programming and Computer Software 8(5) (1992) 232-233)

13. S.V.Chmutov, S.V.Duzhin, Gaydar's formula for greatest common divisor of polynomials in several variables, Uspehi mat. nauk 48 No.2 (1993) 177-178. (in Russian)

( English translation: Russian Mathematical Surveys. 48 (1993) 171-172)

14. S.V.Chmutov, I.G.Scherback, Dynkin diagrams of dual boundary singularities are dual, Journal of Algebraic Geometry 3 (1994) 449-462.

15. S.V.Chmutov, S.V.Duzhin, An upper bound for the number of Vassiliev knot invariants, Journal of Knot Theoryand its Ramifications. 3 (1994) 141-151.

16. S.V.Chmutov, S.V.Duzhin, S.K.Lando, Vassiliev knot invariants I. Introduction, Adv. in Soviet Math. 21 Singularities and Curves, V.I.Arnold ed. (1994) 117-126.

17. S.V.Chmutov, S.V.Duzhin, S.K.Lando, Vassiliev knot invariants II. Intersection graph conjecture for trees, Adv. in Soviet Math. 21 Singularities and Curves, V.I.Arnold ed. (1994) 127-134.

18. S.V.Chmutov, S.V.Duzhin, S.K.Lando, Vassiliev knot invariants III. Forest algebra and weighted graphs, Adv. in Soviet Math. 21 Singularities and Curves, V.I.Arnold ed. (1994) 135-145.

19. S.Chmutov, V.Goryunov, Kauffman bracket of plane curves, Comm. Math. Physics 182 (1996) 83-103.

20. S.V.Chmutov, A.N.Varchenko, Remarks on the Vassiliev knot invariants coming from sl₂, Topology 36 (1997) 153-178.

21. S.Chmutov, S.Duzhin, Explicit formulas for Arnold's generic curve invariants, in Arnold-Gelfand Mathematical Seminars, Birkhäuser (1997) 125-138.

22. S.Chmutov, V.Goryunov, Polynomial invariants of Legendrian links and plane fronts, Topics in Singularity Theory. V.I.Arnold's 60-th Anniversary Collection, (A. Khovanskii, A. Varchenko, V. Vassiliev, eds.) Amer. Math. Soc. Transl. Ser. 2, 180 (1997) 25-44.

23. S.Chmutov, V.Goryunov, Polynomial invariants of Legendrian links and their fronts, Proceedings of KNOTS'96, World Scintific Publishing Co. (1997) 239-256.

24. S.Chmutov, Combinatorial analog of the Melvin-Morton conjecture, Proceedings of KNOTS'96, World Scientific Publishing Co. (1997) 257-266.

25. S.Chmutov, A proof of Melvin-Morton conjecture and Feynman diagrams, Journal of Knot Theory and its Ramifications 7 (1998) 23-40.

26. S.Chmutov, S.Duzhin, A.Kaishev, Algebra of 3-graphs, Proceedings of the Steklov Institute of Mathematics 221(2) (1998) 157--186, ( in Russian), ( English Translation).

27. S.Chmutov, S.Duzhin, A lower bound for the number of Vassiliev knot invariants, Topology and Applications 92 (1999) 201-223.

28. S.Chmutov, S.Duzhin, Knots and their invariants, Matematicheskoe prosveschenie 5 (1999) 59--93. (in Russian).

29. S.Chmutov, S.Duzhin, The Kontsevich integral, in Encyclopaedia of Mathematics, Supplement II (managing editor M. Hazewinkel), Kluwer academic publishers (1999).

30. S.Chmutov, V.Goryunov, H.Murakami, Regular Legendrian knots and the HOMFLY polynomial of immersed plane curves, Math. Ann. 317 (2000) 389-413.

31. S.Chmutov, S.Duzhin, The Kontsevich integral, Acta Applicandae Mathematicae 66 (2001) 155-190.

32. S.Chmutov, Diagrams of divide knots, Proceedings of the Amer. Math. Soc., 131 (2003) 1623--1627.

33. S.Chmutov, An integral generalization of the Gusein-Zade--Natanzon theorem, Moscow Mathematical Journal, 3(3) (2003) 869--879.

34. S.Chmutov, I.Scherbak On Bethe vectors in the sl_N+1 Gaudin model. International Mathematics Research Notices, 26 (2005) 1583--1600. Preprint arXiv:math.RT/0407367.

35. S.Chmutov, I.Pak, The Kauffman bracket of virtual links and the Bollobás-Riordan polynomial. Moscow Mathematical Journal, 7(3) (2007) 409--418. Preprint arXiv:math.GT/0609012.
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36. S.V.Chmutov, S.K.Lando, Mutant knots and intersection graphs. Algebraic and Geometric Topology, 7 (2007) 1579--1598. Preprint arXiv:math.GT/0704.1313.
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37. M.Chmutov, S.Chmutov, Y.Rong, Knight move for chromatic graph homology. European Journal of Combinatorics, 29 (2008) 311--321. Preprint arXiv:math.CO/0511598.
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38. S.Chmutov, J.Voltz, Thistlethwaite's theorem for virtual links. Journal of Knot Theory and its Ramifications, 17(10) (2008) 1189--1198. Preprint arXiv:math.GT/0704.1310.
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39. S.Chmutov, Generalized duality for graphs on surfaces and the signed Bollobás-Riordan polynomial. Journal of Combinatorial Theory, Ser. B, 99(3) (2009) 617--638. Preprint arXiv:0711.3490v3 [math.CO]. PDF file

40. S.Chmutov, M.Khoury, A.Rossi, Polyak-Viro formulas for coefficients of the Conway polynomial. Journal of Knot Theory and its Ramifications, 18(6) (2009) 773--783. Preprint arXiv:0810.3146v1 [math.GT]. PDF file

41. S.Chmutov, M.Polyak, Elementary combinatorics of the HOMFLYPT polynomial. International Mathematics Research Notices, 2010(3) (2010) 480--495. Preprint arXiv:0810.4105v2 [math.GT]. PDF file

42. R.Bradford, C.Butler, S.Chmutov, Arrow ribbon graphs. Journal of Knot Theory and its Ramifications, 21(13) (2012) # 1240002 (16 pages). Preprint arXiv:1107.3237v2 [math.CO].

43. S.Chmutov, B.Pittel, The genus of a random chord diagram is asymptotically normal. Journal of Combinatorial Theory, Ser. A, 120 (2013) 102--110. Preprint arXiv:1108.5214v3 [math.CO].

44. R.Askanazi, S.Chmutov, C.Estill, J.Michel, P.Stollenwerk, Polynomial invariants of graphs on surfaces. Quantum Topology, 3(3) (2013) 77--90. Preprint arXiv:1012.5053v2[math.CO]. .

45. C.Bajo, B.Burdick, S.Chmutov, Tutte-Krushkal-Renardy polynomial for cell complexes. Journal of Combinatorial Theory, Ser. A, 123 (2014) 186--201. Preprint arXiv:1204.3563v4[math.CO].

46. C.Butler, S.Chmutov, Bollobás-Riordan and relative Tutte polynomials. Arnold Mathematical Journal, 1(3) (2015) 283--298. Preprint arXiv:1011.0072v1 [math.CO].

47. S.Chmutov, B.Pittel, On a surface formed by randomly gluing together polygonal discs. Advances in Applied Mathematics, 73 (2016) 23--42. Preprint arXiv:1503.01816 [math.CO].

48. S.Chmutov, S.Jablan, K.Karvounis, S.Lambropoulou, On the knot invariants from the Yokonuma--Hecke algebras. Journal of Knot Theory and its Ramifications, 25(9) (2016) # 1641004 (28 pages). Preprint arXiv:1505.06667 [math.GT].

49. J.Huryn, S.Chmutov, A few more trees the symmetric chromatic function can distinguish. Involve, a Journal of Mathematics, 13(1) (2020) 109--116.

50. S.Chmutov, M.Kazarian, S.Lando, Polynomial graph invariants and the KP hierarchy. Selecta Mathematica, 26(3) (2020) Article 34, 22 pages. Preprint arXiv:1803.09800 [math.CO].

51. S.Chmutov, F.Vignes-Tourneret, On a conjecture of Gross, Mansour and Tucker. European Journal of Combinatorics, 97(3) (2021) doi:j.ejc.2021.103368, 7 pages. Preprint arXiv:2101.09319 [math.CO].

52. S.Chmutov, F.Vignes-Tourneret, Partial Duality of Hypermaps. Arnold Mathematical Journal (2022) doi:s40598-021-00194-8, 24 pages. Preprint arXiv:1409.0632 [math.CO].

CHAPTERS IN EDITED BOOKS.

1. S.Chmutov, Comments to the problems 1972-2, 1974-7, 1975-8, 1979-3, 1980-9, 1980-11, 1981-11, 1981-24, 1983-5, 1984-8, 1993-6, 1993-10, 1993-13, 1994-21 in the book Arnold's problems, Springer & Phasis (2004).

2. S.Chmutov, S.Duzhin, The Kontsevich integral, in the Encyclopedia of Mathematical Physics, eds. J.-P.Françoise, G.L.Naber and S.T.Tsou, Elsevier, Oxford (ISBN 978-0-1251-2666-3), 3 (2006) 231--239.
Preprint arXiv:math.GT/0501040.
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3. S.Chmutov, Combinatorics of Vassiliev invariants.
In Introductory Lectures on Knot Theory (eds. L.Kauffman, S.Lambropoulou, S.Jablan, J.Przytycki). Series on Knots and Everything 46, World Scientific (2011) 54--76.

4. S.Chmutov, Conway polynomial. Chapter 64 in Encyclopedia of Knot Theory. Chapman and Hall/CRC (2020) 625--629. ISBN 9781138297845.

5. S.Chmutov, A.Stoimenov, Vassiliev/Finite Type Invariants. Chapter 82 in Encyclopedia of Knot Theory. Chapman and Hall/CRC (2020) 807--814. ISBN 9781138297845.

6. S.Chmutov, Topological Extensions of the Tutte Polynomial. Chapter 27 in Handbook on the Tutte Polynomial and Related Topics. Chapman and Hall/CRC (2022) 497--513. ISBN 9781482240627.