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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. Buchstaberab

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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    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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