The pentagram integrals on inscribed polygons

Richard Evan Schwartz, Serge Tabachnikov

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The pentagram map is a completely integrable system defined on the moduli space of polygons. The integrals for the system are certain weighted homogeneous polynomials, which come in pairs: E1,O2,E2,O2,... In this paper we prove that Ek = Ok for all k, when these integrals are restricted to the space of polygons which are inscribed in a conic section. Our proof is essentially a combinatorial analysis of the integrals.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalElectronic Journal of Combinatorics
Issue number1
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


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