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 http://www.pdmi.ras.ru/~duzhin/papers/: 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 http://www.pdmi.ras.ru/~duzhin/papers/: 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 http://www.pdmi.ras.ru/~duzhin/papers/: 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 http://www.pdmi.ras.ru/~duzhin/papers/: 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 http://www.pdmi.ras.ru/~duzhin/papers/: 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 http://www.pdmi.ras.ru/~duzhin/papers/: 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 http://www.pdmi.ras.ru/~duzhin/papers/: 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 http://www.pdmi.ras.ru/~duzhin/papers/: 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: http://www.pdmi.ras.ru/~duzhin/papers/cdk.ps.gz (Russian), http://www.pdmi.ras.ru/~duzhin/papers/cdk-e.ps.gz (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.
http://www.pdmi.ras.ru/~duzhin/papers/2x2.tex.gz.
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 http://www.pdmi.ras.ru/~duzhin/papers/: abstract, gzipped PostScript.
17. S.Duzhin. On the Kleinian weight systems. ``Low-Dimensional Topology of Tomorrow''. Suurikaisekikenkyuusho Kookyuuroku 1272, June 2002, pp 84--90. http://www.pdmi.ras.ru/~duzhin/papers/kyoto.ps.gz.
18. S.Duzhin. Decomposable skew-symmetric functions. Moscow Mathematical Journal, v. 3, no. 3 (2003), p. 881--888. Online version: http://www.pdmi.ras.ru/~duzhin/papers/skew_fun.ps.gz.
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:
arXiv.org/abs/1001.2500.
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: arXiv.org/abs/1105.1264. Locally kept copy: PDF, sources.
2. S.Duzhin, D.Pasechnik. Automorphisms of necklaces and sandpile groups. arXiv:1304.2563.
2. Henkangun nyuumon, Springer Verlag Tokyo, 2000; second printing, 2002. (Updated Japanese translation of [1]). Draft version is available online at http://www.pdmi.ras.ru/~duzhin/Ornam/.
3. Transformation groups for beginners, AMS, Student Mathematical Library 25, 2004, 246 pp. (Updated English translation of [1]). Draft version is available online at http://www.pdmi.ras.ru/~duzhin/Ornam/.
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 http://www.pdmi.ras.ru/~duzhin/Vics/vics.ps.gz.
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.
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 http://www.pdmi.ras.ru/~duzhin/papers/. 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 http://www.pdmi.ras.ru/~duzhin/papers/: 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 http://www.pdmi.ras.ru/~duzhin/papers/dk-ccg.tex.gz.
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 http://www.pdmi.ras.ru/~duzhin/papers/kn96.zip.
11. S.Duzhin. "Seminar Diary" column in "Suugaku seminar" (Tokyo), a set of 12 essays, April 1996 -- March 1997 (in Japanese). Online at http://www.pdmi.ras.ru/~duzhin/papers/suusemi.jis.gz (Japanese), http://www.pdmi.ras.ru/~duzhin/papers/suusemi.eng.gz (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
http://www.pdmi.ras.ru/~duzhin/papers/mati-pol.ps.gz.
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.)
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;//http://trv-science.ru/2012/05/22/chto-zhe-dokazal-grigorijj-perelman/,
а также
pdf file,
исходники.
20.
С.В.Дужин. Перечисление деревьев. Математическое просвещение. Сер.3,
вып.16, 2012. С. 14-25. См. http://www.mccme.ru/free-books/matpros.
(Локальные копии файлов: LaTeX.
pdf.)
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.
http://mathworld.wolfram.com/KontsevichIntegral.html
23.
Duzhin, Sergei. "Vassiliev Invariant."
From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.
http://mathworld.wolfram.com/VassilievInvariant.html
14.
S.Duzhin. On integrability of dynamical systems in the real Plane. Prod.
Conf. Quantum Topology, Magnitorosk, July 15-18, 2014.
PDF file,
TeX source.
(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.)
Back to Duzhin's home-page.