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Trudy Mat. Inst. Steklova, 2008, Volume 263, Pages 18–43 (Mi tm781)  

This article is cited in 16 scientific papers (total in 17 papers)

Ring of Simple Polytopes and Differential Equations

V. M. Buchstaberab

a Steklov Mathematical Institute, Russian Academy of Sciences
b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: Simple polytopes are a classical object of convex geometry. They play a key role in many modern fields of research, such as algebraic and symplectic geometry, toric topology, enumerative combinatorics, and mathematical physics. In this paper, the results of a new approach based on a differential ring of simple polytopes are described. This approach allows one to apply the theory of differential equations to the study of combinatorial invariants of simple polytopes.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 263, 13–37

Bibliographic databases:

UDC: 515.164.8
Received in August 2008

Citation: V. M. Buchstaber, “Ring of Simple Polytopes and Differential Equations”, Geometry, topology, and mathematical physics. I, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 263, MAIK Nauka/Interperiodica, Moscow, 2008, 18–43; Proc. Steklov Inst. Math., 263 (2008), 13–37

Citation in format AMSBIB
\by V.~M.~Buchstaber
\paper Ring of Simple Polytopes and Differential Equations
\inbook Geometry, topology, and mathematical physics.~I
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2008
\vol 263
\pages 18--43
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2008
\vol 263
\pages 13--37

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    This publication is cited in the following articles:
    1. N. Yu. Erokhovets, “Gal's Conjecture for Nestohedra Corresponding to Complete Bipartite Graphs”, Proc. Steklov Inst. Math., 266 (2009), 120–132  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Yu. M. Ustinovskii, “Doubling operation for polytopes and torus actions”, Russian Math. Surveys, 64:5 (2009), 952–954  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. V. M. Buchstaber, N. Yu. Erokhovets, “Algebra of operators on the ring of polytopes and quasi-symmetric functions”, Russian Math. Surveys, 65:2 (2010), 381–383  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. M. A. Gorsky, “Proof of Gal's conjecture for the $D$ series of generalized associahedra”, Russian Math. Surveys, 65:6 (2010), 1178–1180  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. V. M. Buchstaber, N. Yu. Erokhovets, “Polytopes, Fibonacci numbers, Hopf algebras, and quasi-symmetric functions”, Russian Math. Surveys, 66:2 (2011), 271–367  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. V. M. Buchstaber, V. D. Volodin, “Sharp upper and lower bounds for nestohedra”, Izv. Math., 75:6 (2011), 1107–1133  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. A. A. Aizenberg, V. M. Buchstaber, “Nerve complexes and moment–angle spaces of convex polytopes”, Proc. Steklov Inst. Math., 275 (2011), 15–46  mathnet  crossref  mathscinet  isi  elib  elib
    8. A. M. Vershik, A. P. Veselov, A. A. Gaifullin, B. A. Dubrovin, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, D. V. Millionshchikov, S. P. Novikov, T. E. Panov, A. G. Sergeev, I. A. Taimanov, “Viktor Matveevich Buchstaber (on his 70th birthday)”, Russian Math. Surveys, 68:3 (2013), 581–590  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. M. Deza, M. Dutour Sikirić, M. I. Shtogrin, “Fullerenes and disk-fullerenes”, Russian Math. Surveys, 68:4 (2013), 665–720  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. N. Yu. Erokhovets, “Buchstaber invariant theory of simplicial complexes and convex polytopes”, Proc. Steklov Inst. Math., 286 (2014), 128–187  mathnet  crossref  crossref  isi  elib  elib
    11. M. Bakuradze, “On the Buchstaber formal group law and some related genera”, Proc. Steklov Inst. Math., 286 (2014), 1–15  mathnet  crossref  crossref  isi  elib  elib
    12. V. M. Buchstaber, A. V. Ustinov, “Coefficient rings of formal group laws”, Sb. Math., 206:11 (2015), 1524–1563  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    13. G. Yu. Panina, I. Streinu, “Virtual polytopes”, Russian Math. Surveys, 70:6 (2015), 1105–1165  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. A. A. Gaifullin, “Small covers of graph-associahedra and realization of cycles”, Sb. Math., 207:11 (2016), 1537–1561  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    15. Bakuradze M., Jibladze M., “Some explicit expressions concerning BP”, Georgian Math. J., 23:2 (2016), 157–167  crossref  mathscinet  zmath  isi  elib  scopus
    16. Grujic V., “Quasisymmetric Functions For Nestohedra”, SIAM Discret. Math., 31:4 (2017), 2570–2585  crossref  mathscinet  zmath  isi  scopus
    17. V. M. Buchstaber, I. Yu. Limonchenko, “Massey products, toric topology and combinatorics of polytopes”, Izv. Math., 83:6 (2019), 1081–1136  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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