A Construction of Short Sequences Containing All Permutations of a Set as Subsequences
Keywords:
Combinatorics on Words, Shortest Sequences, Permutations
Abstract
A sequence over a fixed finite set is said to be complete if it contains all permutations of the set as subsequences. Determining the length of shortest complete sequences is an open problem. We improve the existing upper bound and introduce tools to manually prove the completeness of sequences.