A new approach to cross-bifix-free sets

TL;DR

This paper introduces a new constructive method for generating cross-bifix-free binary word sets of fixed length, including a way to identify non-expandable subsets, advancing combinatorial word theory.

Contribution

The paper presents a novel constructive approach to generate and analyze cross-bifix-free sets, including a method to find non-expandable subsets.

Findings

Developed a general method for constructing cross-bifix-free sets

Identified criteria for non-expandable cross-bifix-free subsets

Enhanced understanding of combinatorial properties of such sets

Abstract

Cross-bifix-free sets are sets of words such that no prefix of any word is a suffix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free binary words of fixed length. It enables us to determine a cross-bifix-free words subset which has the property to be non-expandable.