Pattern avoidance in partial words over a ternary alphabet

Adam Gagol
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引用次数: 1

Abstract

Blanched-Sadri and Woodhouse in 2013 have proven the conjecture of Cassaigne, stating that any pattern with \(m\) distinct variables and of length at least \(2^m\) is avoidable over a ternary alphabet and if the length is at least \(3\cdot 2^{m-1}\) it is avoidable over a binary alphabet. They conjectured that similar theorems are true for partial words – sequences, in which some characters are left “blank”. Using method of entropy compression, we obtain the partial words version of the theorem for ternary words.
三元字母表上部分单词的模式避免
blanche - sadri和Woodhouse在2013年证明了casassaigne的猜想,指出任何具有\(m\)不同变量且长度至少为\(2^m\)的模式在三元字母表中都是可避免的,如果长度至少为\(3\cdot 2^{m-1}\),则在二进制字母表中是可避免的。他们推测,类似的定理也适用于部分词序列,其中一些字符是“空白”的。利用熵压缩的方法,我们得到了三元词定理的部分词版本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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