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

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Volume 263, Pages 18–43 (Mi tm781)

This article is cited in 21 scientific papers (total in 22 papers)

Ring of Simple Polytopes and Differential Equations

V. M. Buchstaber^ab

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

Full-text PDF (362 kB) Citations (22)

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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.

Received in August 2008

English version:
Proceedings of the Steklov Institute of Mathematics, 2008, Volume 263, Pages 13–37
DOI: https://doi.org/10.1134/S0081543808040032

Bibliographic databases:

Document Type: Article

UDC: 515.164.8

Language: Russian

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

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Linking options:

https://www.mathnet.ru/eng/tm781

https://www.mathnet.ru/eng/tm/v263/p18

This publication is cited in the following 22 articles:

V. M. Buchstaber, “Polynomial Eulerian characteristic of nilmanifolds”, Funct. Anal. Appl., 58:1 (2024), 16–32
Anton Ayzenberg, Victor Buchstaber, “Cluster-permutohedra and submanifolds of flag varieties with torus actions”, Int. Math. Res. Not. IMRN, 2024:3 (2024), 1931–1967
Ivan Limonchenko, Dmitry Millionshchikov, Contemporary Mathematics, 772, Topology, Geometry, and Dynamics, 2021, 209
V. M. Buchstaber, I. Yu. Limonchenko, “Massey products, toric topology and combinatorics of polytopes”, Izv. Math., 83:6 (2019), 1081–1136
Grujic V., “Quasisymmetric Functions For Nestohedra”, SIAM Discret. Math., 31:4 (2017), 2570–2585
A. A. Gaifullin, “Small covers of graph-associahedra and realization of cycles”, Sb. Math., 207:11 (2016), 1537–1561
Bakuradze M., Jibladze M., “Some explicit expressions concerning BP”, Georgian Math. J., 23:2 (2016), 157–167
V. M. Buchstaber, A. V. Ustinov, “Coefficient rings of formal group laws”, Sb. Math., 206:11 (2015), 1524–1563
G. Yu. Panina, I. Streinu, “Virtual polytopes”, Russian Math. Surveys, 70:6 (2015), 1105–1165
N. Yu. Erokhovets, “Buchstaber invariant theory of simplicial complexes and convex polytopes”, Proc. Steklov Inst. Math., 286 (2014), 128–187
M. Bakuradze, “On the Buchstaber formal group law and some related genera”, Proc. Steklov Inst. Math., 286 (2014), 1–15
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
M. Deza, M. Dutour Sikirić, M. I. Shtogrin, “Fullerenes and disk-fullerenes”, Russian Math. Surveys, 68:4 (2013), 665–720
Polytope Projects, 2013, 17
Octavian Iordache, Understanding Complex Systems, Self-Evolvable Systems, 2012, 31
V. M. Buchstaber, N. Yu. Erokhovets, “Polytopes, Fibonacci numbers, Hopf algebras, and quasi-symmetric functions”, Russian Math. Surveys, 66:2 (2011), 271–367
V. M. Buchstaber, V. D. Volodin, “Sharp upper and lower bounds for nestohedra”, Izv. Math., 75:6 (2011), 1107–1133
A. A. Aizenberg, V. M. Buchstaber, “Nerve complexes and moment–angle spaces of convex polytopes”, Proc. Steklov Inst. Math., 275 (2011), 15–46
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
M. A. Gorsky, “Proof of Gal's conjecture for the $D$ series of generalized associahedra”, Russian Math. Surveys, 65:6 (2010), 1178–1180

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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