Search Algorithms for the Combinatorial Generation of Bordered Box Repetition-Free Words

Four search algorithms to search for the longest box repetition-free word over a given alphabet are presented, giving an empirical result on the upper bound of the length of these words. A box repetition-free word is a finite word w where any given factor of the form asa, with a ∈ Σ and s ∈ Σ∗, occurs at most once. A maximal box repetition-free word is a box repetition-free word which cannot be extended by appending to it any a ∈ Σ without it ceasing to be repetition free.