Positivity of denominator vectors of cluster algebras

TL;DR

This paper proves that denominator vectors in skew-symmetric cluster algebras always have positive entries, confirming a key property in the structure of these mathematical objects.

Contribution

It establishes the positivity of denominator vectors for all skew-symmetric cluster algebras, a previously unproven property.

Findings

Positivity of denominator vectors proven for all skew-symmetric cluster algebras

Confirms a key structural property of these algebras

Supports further theoretical developments in cluster algebra theory

Abstract

In this paper, we prove that positivity of denominator vectors holds for any skew-symmetric cluster algebra.