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BIRS Workshop Lecture Videos

On a scissors congruence phenomenon for some polytopes Ramirez Alfonsin, Jorge


The scissors congruence conjecture for the unimodular group is an analogue of Hilberts third problem, for the equidecomposability of polytopes. In this talk, we present a proof of this conjecture for polytopes naturally associated to graphs whose vertices have degree one or three. The key ingredient in the proof is the nearest neighbor interchange on graphs and a naturally arising piecewise unimodular transformation. We also discuss some Ehrhart quasi-polynomials results for this class of polytopes (joint work with C.G. Fernandes, J.C. de Pina and S. Robins).

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