Some Tribonacci Conjectures

TL;DR

This paper demonstrates how to verify or refute conjectures related to the infinite Tribonacci word using the Walnut theorem-prover, providing a mechanical approach to combinatorial word problems.

Contribution

It introduces a method to mechanically prove or disprove Tribonacci word conjectures using the Walnut theorem-prover, simplifying complex combinatorial proofs.

Findings

Successfully verified several Tribonacci word conjectures

Provided a systematic approach for future combinatorial word conjecture testing

Enhanced understanding of the structure of the infinite Tribonacci word

Abstract

In a recent talk of Robbert Fokkink, some conjectures related to the infinite Tribonacci word were stated by the speaker and the audience. In this note we show how to prove (or disprove) the claims easily in a "purely mechanical" fashion, using the Walnut theorem-prover.