A partial answer to the Demyanov-Ryabova conjecture

Aris Daniilidis; Colin Petitjean

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arXiv · 1702.00168

A partial answer to the Demyanov-Ryabova conjecture

Aris Daniilidis·Colin Petitjean

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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".

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Aris Daniilidis, Colin Petitjean. 2017-02-01. A partial answer to the Demyanov-Ryabova conjecture. https://arxiv.org/abs/1702.00168

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