The Demyanov-Ryabova conjecture is false

TL;DR

This paper disproves the Demyanov-Ryabova conjecture by providing a counterexample where the minimal cycle length exceeds two, specifically demonstrating a cycle length of four.

Contribution

The authors construct the first known counterexample to the conjecture, showing that the minimal cycle length can be greater than two.

Findings

Counterexample with cycle length 4

Disproof of the conjecture

Minimal cycle length can be greater than two

Abstract

It was conjectured by Vladimir Demyanov and Julia Ryabova in 2011 that the minimal cycle in the sequence obtained via repeated application of Demyanov converter to a finite family of polytopes is at most two. We construct a counterexample for which the minimal cycle has length 4.