Ring of simple polytopes and differential equations

V. M. Buchstaber

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)13-37
Number of pages25
JournalProceedings of the Steklov Institute of Mathematics
Issue number1
Publication statusPublished - Dec 2008
Externally publishedYes


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