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On equidissection of balanced polygons

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arxiv 1206.4591 v2 pith:KHCCB7TX submitted 2012-06-20 math.CO math.AG

classification math.COmath.AG
keywords balancedareascannotequalequidissectionnumberpolygontriangles
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In this paper we show that a lattice balanced polygon of odd area cannot be cut into an odd number of triangles of equal areas. First result of this type was obtained by Paul Monsky in 1970. He proved that a square cannot be cut into an odd number of triangles of equal areas. In 2000 Sherman Stein conjectured that the same holds for any balanced polygon. We also show connections between the equidissection problem and tropical geometry.

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