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Uspekhi Mat. Nauk, 1992, Volume 47, Issue 1(283), Pages 3–45 (Mi umn4470)  

This article is cited in 25 scientific papers (total in 26 papers)

The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups

V. I. Arnol'd

Steklov Mathematical Institute, Russian Academy of Sciences

Full text: PDF file (2446 kB)
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English version:
Russian Mathematical Surveys, 1992, 47:1, 1–51

Bibliographic databases:

UDC: 512.761+515.164.15
MSC: 05A19, 11B68, 20F55, 37J20, 05A05
Received: 21.10.1991

Citation: V. I. Arnol'd, “The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups”, Uspekhi Mat. Nauk, 47:1(283) (1992), 3–45; Russian Math. Surveys, 47:1 (1992), 1–51

Citation in format AMSBIB
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\by V.~I.~Arnol'd
\paper The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups
\jour Uspekhi Mat. Nauk
\yr 1992
\vol 47
\issue 1(283)
\pages 3--45
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\transl
\jour Russian Math. Surveys
\yr 1992
\vol 47
\issue 1
\pages 1--51
\crossref{https://doi.org/10.1070/RM1992v047n01ABEH000861}
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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. V. I. Arnol'd, “Congruences for Euler, Bernoulli, and Springer numbers of Coxeter groups”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 389–393  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. A. Glutsyuk, “An analogue of Cayley's theorem for cyclic symmetric connected graphs with one cycle connected with generalized Lyashko–Looijenga covers”, Russian Math. Surveys, 48:2 (1993), 182–183  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. A. Glutsyuk, “An analogue of Cayley's theorem for cyclically symmetric connected graphs with a single cycle that are associated with generalized Lyashko–Looijenga covers”, Russian Math. Surveys, 48:4 (1993), 247–248  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. A. Kirillov, “On the Combinatorics of Coadjoint Orbits”, Funct. Anal. Appl., 27:1 (1993), 62–64  mathnet  crossref  mathscinet  zmath  isi
    5. M. R. Entov, “Number of Components of the Set of Real Morsifications of $D_\mu$ Singularities”, Funct. Anal. Appl., 27:2 (1993), 151–154  mathnet  crossref  mathscinet  zmath  isi
    6. M. R. Entov, “On the real preimages of a real point under the Liashko–Looijenga covering for simple singularities”, Russian Acad. Sci. Izv. Math., 43:2 (1994), 363–372  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. G. Kuznetsov, I. M. Pak, A. E. Postnikov, “Increasing trees and alternating permutations”, Russian Math. Surveys, 49:6 (1994), 79–114  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. G. G. Ilyuta, “Geometric constructions of higher Bruhat orders and $M$-Morsifications”, Izv. Math., 60:6 (1996), 1183–1192  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. V. I. Arnol'd, “Topological Classification of Trigonometric Polynomials and Combinatorics of Graphs with an Equal Number of Vertices and Edges”, Funct. Anal. Appl., 30:1 (1996), 1–14  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. G. G. Ilyuta, “Coxeter–Dynkin Diagrams of Partially Ordered Sets and A'Campo–Gusein-Zade Diagrams of Simple Singularities”, Funct. Anal. Appl., 31:1 (1997), 10–15  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. D. V. Anosov, A. A. Bolibrukh, V. A. Vassiliev, A. M. Vershik, A. A. Gonchar, M. L. Gromov, S. M. Gusein-Zade, V. M. Zakalyukin, Yu. S. Ilyashenko, V. V. Kozlov, M. L. Kontsevich, Yu. I. Manin, A. I. Neishtadt, S. P. Novikov, Yu. S. Osipov, M. B. Sevryuk, Ya. G. Sinai, A. N. Tyurin, L. D. Faddeev, B. A. Khesin, A. G. Khovanskii, “Vladimir Igorevich Arnol'd (on his 60th birthday)”, Russian Math. Surveys, 52:5 (1997), 1117–1139  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    12. G. G. Ilyuta, “Lagrange Interpolation with Respect to Chebyshev Systems and Higher Bruhat Orders”, Funct. Anal. Appl., 32:3 (1998), 203–205  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. Phys. Usp., 42:12 (1999), 1205–1217  mathnet  crossref  crossref  isi  elib
    14. G. G. Ilyuta, “A'Campo–Gusein-Zade diagrams as partially ordered sets”, Izv. Math., 65:4 (2001), 687–704  mathnet  crossref  crossref  mathscinet  zmath  elib
    15. B. Z. Shapiro, A. D. Vainshtein, “Counting real rational functions with all real critical values”, Mosc. Math. J., 3:2 (2003), 647–659  mathnet  mathscinet  zmath  elib
    16. Boris Shapiro, Michael Shapiro, Alek Vainshtein, “Periodic de Bruijn triangles: exact and asymptotic results”, Discrete Mathematics, 298:1-3 (2005), 321  crossref
    17. Vladimir I. Arnold, “Topological Classification of Morse Functions and Generalisations of Hilbert’s 16-th Problem”, Math Phys Anal Geom, 10:3 (2007), 227  crossref  mathscinet  zmath  isi  elib
    18. Piergiulio Tempesta, “On Appell sequences of polynomials of Bernoulli and Euler type”, Journal of Mathematical Analysis and Applications, 341:2 (2008), 1295  crossref
    19. E. I. Bravyi, “Razreshimost rezonansnykh kraevykh zadach dlya funktsionalno-differentsialnykh uravnenii s monotonnymi operatorami”, Trudy shestoi Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem (1–4 iyunya 2009 g.). Chast 3, Differentsialnye uravneniya i kraevye zadachi, Matem. modelirovanie i kraev. zadachi, SamGTU, Samara, 2009, 55–57  mathnet
    20. Matthieu Josuat-Vergès, Jean-Christophe Novelli, Jean-Yves Thibon, “The algebraic combinatorics of snakes”, Journal of Combinatorial Theory, Series A, 119:8 (2012), 1613  crossref
    21. E. A. Kudryavtseva, “The Topology of Spaces of Morse Functions on Surfaces”, Math. Notes, 92:2 (2012), 219–236  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    22. Bravyi E.I., “O nailuchshikh konstantakh v usloviyakh razreshimosti periodicheskoi kraevoi zadachi dlya funktsionalno-differentsialnykh uravnenii vysshikh poryadkov”, Differentsialnye uravneniya, 48:6 (2012), 773–773  elib
    23. E. A. Kudryavtseva, “On the homotopy type of spaces of Morse functions on surfaces”, Sb. Math., 204:1 (2013), 75–113  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    24. Huilan Chang, Sen-Peng Eu, Yuan-Hsun Lo, “Sign imbalances of snakes and valley-signed permutations”, Advances in Applied Mathematics, 59 (2014), 26  crossref
    25. Matthieu Josuat-Vergès, “A Generalization of Euler Numbers to Finite Coxeter Groups”, Ann. Comb, 2015  crossref
    26. V. E. Aksenov, K. P. Kokhas, “Calculation of Pfaffians by a chip removal”, J. Math. Sci. (N. Y.), 215:6 (2016), 631–648  mathnet  crossref  mathscinet
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