Computing Non-Repetitive Sequences with a Computable Lefthanded Local Lemma

TL;DR

This paper develops a computable version of the lefthanded Lovász local lemma (LLLL) and uses it to constructively prove the existence of certain non-repetitive sequences, advancing the application of probabilistic combinatorics.

Contribution

It introduces the first constructive proof of non-repetitive sequences using a computable LLLL, extending the applicability of the probabilistic method.

Findings

First constructive proof of non-repetitive sequences via LLLL

Development of a computable version of the LLLL

Application of the computable LLLL to combinatorial sequence problems

Abstract

The lefthanded Lov\'asz local lemma (LLLL) is a generalization of the Lov\'asz local lemma (LLL), a powerful technique from the probabilistic method. We prove a computable version of the LLLL and use it to effectivize a collection of results on the existence of certain types of non-repetitive sequences via the LLL and LLLL. This represents the first constructive proof of these results.