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Let g 1 ,. .. , g k be tropical polynomials in n variables with Newton polytopes P 1 ,. .. , P k. We study combinatorial questions on the intersection of the tropical hyper-surfaces defined by g 1 ,. .. , g k , such as the f-vector, the number of unbounded faces and (in case of a curve) the genus. Our point of departure is Vigeland's work [33] who(More)
The aim of this thesis is the discussion of mixed volumes, their interplay with algebraic geometry, discrete geometry and tropical geometry and their use in applications such as linkage configuration problems. Namely we present new technical tools for mixed volume computation, a novel approach to Ehrhart theory that links mixed volumes with counting integer(More)
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