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{\bf Richard Evan Schwartz and Serge Tabachnikov}
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{\bf The Pentagram Integrals on Inscribed Polygons}
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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: $E_1,O_2,E_2,O_2,\dots$  In this paper we
prove that $E_k=O_k$ 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.

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