Extremal Pattern-Avoiding Words [article]

Natalya Ter-Saakov, Emily Zhang
2020 arXiv   pre-print
Recently, Grytczuk, Kordulewski, and Niewiadomski defined an extremal word over an alphabet 𝔸 to be a word with the property that inserting any letter from 𝔸 at any position in the word yields a given pattern. In this paper, we determine the number of extremal XY_1XY_2X... XY_tX-avoiding words on a k-letter alphabet. We also derive a lower bound on the shortest possible length of an extremal square-free word on a k-letter alphabet that grows exponentially in k.
arXiv:2009.10186v1 fatcat:wjhfogz4jbheppds7zae4ca5ea