THE LENGTH OF SHORT WORDS IN UNAVOIDABLE SETS
Peter M. Higgins · International Journal of Algebra and Computation · 2011
Maximum possible lengths of short words in unavoidable sets of order no more than n have the form log n + O( log log n). The respective log bases of the upper and lower bounds of the shortest and second shortest words are (for a two-letter alphabet) 2 and τ, the Golden Ratio. The latter result comes through identifying certain bases of free monoids.