UNAVOIDABLE SETS OF CONSTANT LENGTH

JEAN-MARC CHAMPARNAUD, GEORGES HANSEL, DOMINIQUE PERRIN
2004 International journal of algebra and computation  
A set of words X is called unavoidable on a given alphabet A if every infinite word on A has a factor in X. For k, q ≥ 1, let c(k, q) be the number of conjugacy classes of words of length k on q letters. An unavoidable set of words of length k on q symbols has at least c(k, q) elements. We show that for any k, q ≥ 1 there exists an unavoidable set of words of length k on q symbols having c(k, q) elements.
doi:10.1142/s0218196704001700 fatcat:do7ozqsadbcojh46f3limxwl2m