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In this note, we study B{\'e}zout type inequalities for mixed volume andMinkowski sum of convex bodies in R n. We first give a new proof and we extendinequalities of Jian Xiao on mixed discriminants. Then, we use mass transportmethod to deduce some B{\'e}zout type inequalities for mixed volumes. Finally,we apply these inequalities to obtain B{\'e}zout type inequalities forMinkowski sums.

A note on B{\'e}zout type inequalities for mixed volumes and Minkowski sums