Sergei V. Duzhin

List of publications and manuscripts

Research articles published in refereed journals

1. S.V.Duzhin. A C-spectral sequence on the manifold J^1(M). Uspehi mat. nauk, 1983, v. 38, n.1, p. 165--166 (Russian; English transl. in Russian Math. Surveys, 38:1, p. 179--181).

2. S.V.Duzhin. A spectral sequence associated with a foliation, and Gelfand-Fuks cohomology of certain Lie algebras of vector fields. - Uspehi mat. nauk, 1984, v. 39, n.1, p. 135--136 (Russian; English transl. in Russian Math. Surveys, 39:1, p. 147--148).

3. S.V.Duzhin, T.Tsujishita. Conservation laws of the BBM equation. --- J. Phys. A: Math. Gen., v. 17 (1984), p. 3267--3276.

4. S.V.Duzhin, V.V.Lychagin. Symmetries of distributions and quadrature of ordinary differential equations. --- Acta Applicandae Mathematicae, v.24, p. 29--57, 1991. Online at abstract, plain TeX, gzipped PostScript.

5. S.V.Duzhin, S.V.Chmutov. Gaydar's formula for the greatest common divisor of several multivariate polynomials. Uspekhi Mat. Nauk, v. 48, no. 2, p. 177--178, 1993 (Russian; English translation in Russian Math. Surveys 48, no.2, 171--172, 1993). Online at abstract, Plain TeX (Russian in AMS encoding), gzipped PostScript.

6. G.Carra`-Ferro, S.V.Duzhin. Differential-algebraic and differential-geometric approach to the study of involutive symbols.-- In: N.H.Ibragimov et al. (eds.), Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics, 93--99, Kluwer Academic Publishers, 1993.

7. S.V.Chmutov, S.V.Duzhin. An upper bound for the number of Vassiliev knot invariants. --- Journal of Knot Theory and its Ramifications. v.3, 141--151, 1994. Online at abstract, gzipped PostScript.

8. S.V.Chmutov, S.V.Duzhin, S.K.Lando. Vassiliev knot invariants I. Introduction. --- Adv. in Soviet Math., v.21. Singularities and Curves, V.I.Arnold ed. (1994) 117-126. Online at abstract, gzipped PostScript.

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

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

11. S.Chmutov, S.Duzhin. Explicit formulas for Arnold's generic curve invariants, In: ``Arnold-Gelfand Mathematical Seminars: Geometry and Singularity Theory." Birkhauser, 1997, p. 123--138. Online at abstract, gzipped PostScript.

12. S.V.Chmutov, S.V.Duzhin. A lower bound for the number of Vassiliev knot invariants. "Topology and its Applications" 92 (1999) 201--223. Online at abstract, gzipped PostScript.

13. S.V.Chmutov, S.V.Duzhin, A.I.Kaishev. The algebra of 3-graphs. Trudy Matematicheskogo Instituta im. Steklova, v. 221 (1998), pp.168--196. English translation: Trans. Steklov Math. Inst., v. 221 (1998), pp.157--186. Abstract. Full text: (Russian), (English),

14. S.V.Duzhin, A.I.Kaishev. T-system implementation of the program of computation of sl- and so-polynomials for 3-graphs. In: "Programmnye sistemy" (transactions of Program Systems Institute, Pereslavl-Zalessky), Moscow, Nauka, Fizmatlit, 1999, p. 214-223 (in Russian).

15. S.V.Duzhin. Infinitesimal classification of systems of two first order partial differential equations. Zapiski POMI, v. 279, p. 61--69, St.Petersburg, 2001 (in Russian). abstract, LaTeX, PostScript.
English translation: Journal of Mathematical Sciences, January 2004, Volume 119, Issue 1, pp. 30-34.

16. S.V.Chmutov, S.V.Duzhin. The Kontsevich integral. Acta Applicandae Math. 66 (2), p. 155--190, April 2001. Preprint version (1997-1999) is available at abstract, gzipped PostScript.

17. S.Duzhin. On the Kleinian weight systems. ``Low-Dimensional Topology of Tomorrow''. Suurikaisekikenkyuusho Kookyuuroku 1272, June 2002, pp 84--90.

18. S.Duzhin. Decomposable skew-symmetric functions. Moscow Mathematical Journal, v. 3, no. 3 (2003), p. 881--888. Online version:

19. S.Chmutov, S.Duzhin. The Kontsevich integral. Encyclopedia of Mathematical Physics, eds. J.-P.Francoise, G.L.Naber and S.T.Tsou. Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3), volume 3, pp. 231--239. Draft version online at arXiv:math.GT/0501040.

20. S.Duzhin, J.Mostovoy. A toy theory of Vassiliev invariants. Moscow Mathematical Journal 6(1), p. 85-93 (2006). gzipped Postscript.

21. S.V.Duzhin, M.V.Karev. Detecting the orientation of string links by finite type invariants. Funct. Anal. Appl., v. 41, no. 3, 48--59, 2007.
(Russian original: С.В.Дужин, М.В.Карев. Определение ориентации струнных зацеплений при помощи инвариантов конечного типа. Функц. анализ и его приложения , т. 41, вып. 3, стр. 48--59, 2007).
Preprint version (July 1, 2005): arXiv:math.GT/0507015.
Updated Russian version: postscript, TeX and xfig sources.
Updated English version: pdf,

22. С.В.Дужин. Многочлен Конвея и разложение Магнуса. Алгебра и Анализ, том 23 (2011), вып. 3, с. 175--188. (English translation: S.Duzhin. Conway polynomial and Magnus expansion. St.Petersburg Math. Journal, v.23 (2012), no.3, pp. 541--550.)
Preprint version:
Updated drafts: Russian pdf, English pdf, sources (zip).

23. С.В.Дужин. Доказательство гипотезы Пшитыцкого о парных диаграммах. ДАН, Математика, т. 441, вып. 2, с. 156--157 (2011). (English translation: Proof of Przytycki's conjecture on matched diagrams.) Doklady Mathematics, vol. 84, no. 3, p. 787--788, 2011). Russian pdf, LaTeX sources (Russian). English pdf.

24. С.В.Дужин. Алгоритмы вычисления полинома Конвея по двудольному графу. Информационно-управляющие системы, N4 (2011), стр. 89--91. (S.V.Duzhin, Algorithms for the computations of the Conway polynomial from a bipartite graph. Information and Control Systems, no.4 (2011), 89--91). Russian pdf, LaTeX sources.

25. S.V.Duzhin, D.V.Pasechnik. Groups acting on necklaces and sandpile groups. Zapiski nauch seminarov POMI 421 (2014), 81--93. (In English). To be reprinted in "Journal of mathematical sciences" (Springer) in 2014.

26. Bipartite knots, by S. Duzhin and M. Shkolnikov. Fundamenta Math. vol. 225, 95--102 (2014), pdf file. Preprint version: Locally kept copy: PDF, sources.


1. A formula for the HOMFLY polynomial of rational links, by S.Duzhin and M.Shkolnikov. September 2010, updated October 2010. Locally kept copy: PDF, sources.

2. S.Duzhin, D.Pasechnik. Automorphisms of necklaces and sandpile groups. arXiv:1304.2563.

Books and book chapters

1. From ornaments to differential equations (an introduction to the theory of transformation groups). In Russian. By S.V.Duzhin and B.D.Chebotarevsky. Minsk, Vysheishaya Shkola, 1988, 253 pp. DejaVu file.

2. Henkangun nyuumon, Springer Verlag Tokyo, 2000; second printing, 2002. (Updated Japanese translation of [1]). Draft version is available online at

3. Transformation groups for beginners, AMS, Student Mathematical Library 25, 2004, 246 pp. (Updated English translation of [1]). Draft version is available online at

4. Symmetries and Conservation Laws for Differential Equations of Mathematical Physics. By A.Bocharov, A.Verbovetsky, S.Duzhin et al., ed. by A.Vinogradov and I.Krasilshchik. Moscow, Factorial publishers, 1997, 464 pp. ISBN 5-88688-019-4 (in Russian).

5. English translation of [4]: AMS MMONO/182, 1999, 333 pp. ISBN 0-8218-0958-X.

6. Smooth manifolds and observables. By Jet Nestruev (group of authors consisting of A.Astashov, A.Bocharov, S.Duzhin, A.Sosinsky, A.Vinogradov and M.Vinogradov), Moscow, MCCME publishers, 2000 (Russian).

7. English translation of [6]: "Graduate Texts in Mathematics" v.220, Springer, 2002.

8. S.Duzhin. Lectures on Vassiliev knot invariants. Lectures in Mathematical Sciences, The University of Tokyo, vol. 19, 2002. 123 pp. Online at

9. S.Chmutov, S.Duzhin, J.Mostovoy. Introduction to Vassiliev knot invariants. Cambridge University Press, 2012, 504 pp., ISBN 978-1-107-02083-2. The version posted here is a final non-copyedited draft (with some misprints and errors of the paper publication corrected). An earlier preprint version is online at arXiv:1103.5628.

Reviews, conference proceedings, popularization etc

1. S.V.Duzhin. The C-spectral sequence on finite order jet manifolds. VINITI deposited manuscript, 1982 (in Russian).

2. S.V.Duzhin. Deformation cohomology of one-codimensional plane-parallel foliation on a torus, Proc. of XVII Voronezh Winter Math. School, Voronezh, 1983 (in Russian).

3. S.V.Duzhin, V.N.Rubtsov. Geometry of the 4-dimensional cube. "Kvant", 1986, no.6 (in Russian).

4. S.V.Duzhin et al. Some results on the problem of graphs of small diameter. Technical report, 20 p. (in Russian). Pereslavl-Zalessky, 1991.

5. S.V.Duzhin. Varchenko's view of quantum groups. Notes of a talk delivered at V.Arnold's seminar, Moscow University, Nov. 1991, 3 p. Online at plain TeX, gzipped PostScript.

6. S.V.Duzhin, A.I.Kaishev. Computation of the discriminant of the general ternary cubic form and its Newton polyhedron. Technical report (30 p.). PSI, Pereslavl-Zalessky, 1992.

7. S.V.Duzhin. Network school participant's guide to networking terms and abbreviations, 30 p., ICTP (Trieste, Italy), 1992.

8. S.V.Duzhin. Graphes de Moore. Lecture notes, Nov. 1994, 4 pages (in French). Online at abstract, plain TeX, gzipped PostScript.

9. S.V.Duzhin, A.I.Kaishev. Calculation of central generators of the universal enveloping algebras and Vassiliev--Kontsevich weight systems. -- Proceedings of the international workshop "New Computer Technologies in Control Systems" (editors: M.G.Dmitriev, Yu.L.Sachkow). Pereslavl-Zalessky, August 13-16, 1995. Online at

10. S.Duzhin. A quadratic lower bound for the number of primitive Vassiliev invariants. Extended abstract, KNOT'96 Conference/Workshop report, Waseda University, Tokyo, July 1996, p. 52--54. Online at

11. S.Duzhin. "Seminar Diary" column in "Suugaku seminar" (Tokyo), a set of 12 essays, April 1996 -- March 1997 (in Japanese). Online at (Japanese), (English),

12. S.V.Duzhin. S.V.Chmutov. Узлы и их инваринты ("Knots and their invariants", in Russian). "Matematicheskoe Prosveschenie", no. 3, 1999, pp. 59--93. Also available at .

13. S.Chmutov, S.Duzhin. Kontsevich's integral, in Encyclopaedia of Mathematics, Supplement II, Kluwer academic publishers (1999).

14. Comments to 5 problems, in: V.I.Arnold's Problems, Moscow, Phasis 2000, pp. 343, 372, 402, 438, 446 (in Russian). English edition, updated, Springer 2004: comments to 6 problems.

15. S.Duzhin. The Matiyasevich polynomial, four colour theorem and weight systems, Art of low-dimensional topology VI (ed. T.Kohno), Kyoto, 2000, pp. 9--14. On-line at

16. Translation of 7 articles by J.-P.Serre from French into Russian. In: J.-P.Serre. Collected papers, vol. 1, MCCME publishers, Moscow, 2002.

17. S.V.Duzhin. Vassiliev--Goussarov invariants, in: Mathematics of XX century, view from St.Petersburg. Edited by A.M.Vershik. MCCME Publishers, 2010, pp. 87--116 (in Russian). (Инварианты Васильева--Гусарова. В сборнике: Математика XX века. Взгляд из Петербурга. Под редакцией А.М.Вершика. М.: МЦНМО, 2010, стр. 87--116.)
PDF file, TeX source.

18. С.В.Дужин. Комбинаторные аспекты теории инвариантов Васильева. Докторская диссертация, защищена 14.12.2011, утверждена ВАК 13.04.2012. Версия с исправленными опечатками от 4.01.2012: PDF file, TeX sources. Автореферат с исходниками: здесь.

19. С.В.Дужин. Что же доказал Григорий Перельман? "Троицкий вариант" N 10 (104), 22 мая 2012, стр. 6--7. См. http;//, а также pdf file, исходники.

20. С.В.Дужин. Перечисление деревьев. Математическое просвещение. Сер.3, вып.16, 2012. С. 14-25. См. (Локальные копии файлов: LaTeX. pdf.)
(manuscript version: S.Duzhin. Enumeration of trees. Lecture notes of a course in discrete mathematics. Moscow Higher College of Chemistry, 1993. 9 pages (in Russian). LaTeX, Russian in koi8 encoding. gzipped PostScript.)

21. S.Duzhin. On matched diagrams of knots. Alexandroff Readings. International topological conference. Moscow, May 21-25. Astracts, p.21-22.

22. Chmutov, Sergei and Duzhin, Sergei. "Kontsevich Integral." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

23. Duzhin, Sergei. "Vassiliev Invariant." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. 14. S.Duzhin. On integrability of dynamical systems in the real Plane. Prod. Conf. Quantum Topology, Magnitorosk, July 15-18, 2014.

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