Saturation of Rota's basis conjecture

TL;DR

This paper proves an asymptotic version of Rota's basis conjecture using advanced tensor rank techniques, connecting combinatorics with geometric invariant theory.

Contribution

It introduces an asymptotic saturation approach to Rota's basis conjecture leveraging Tao's slice rank and unstable tensors.

Findings

Established an asymptotic saturation form of Rota's basis conjecture

Connected tensor rank methods with combinatorial basis problems

Provided new insights into the geometric invariant theory approach

Abstract

We prove an asymptotic saturation-type version of Rota's basis conjecture. It relies on the connection of Tao's slice rank with unstable tensors from geometric invariant theory.