A partial answer to the Demyanov-Ryabova conjecture

Abstract

In this work we are interested in the Demyanov--Ryabova conjecture for a finite family of polytopes. The conjecture asserts that after a finite number of iterations (successive dualizations), either a 1-cycle or a 2-cycle eventually comes up. In this work we establish a strong version of this conjecture under the assumption that the initial family contains "enough minimal polytopes" whose extreme points are "well placed".