# A partial answer to the Demyanov-Ryabova conjecture

## TL;DR

This paper investigates the Demyanov-Ryabova conjecture for finite polytope families, proving a strong version under specific conditions related to minimal polytopes with well-positioned extreme points.

## Contribution

It establishes a strong version of the conjecture assuming the initial family contains sufficiently many minimal polytopes with well-placed extreme points.

## Key findings

- Proves the conjecture under new conditions
- Demonstrates finite convergence to 1- or 2-cycles
- Provides insights into polytope dualization dynamics

## 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".