三元字母表上部分单词的模式避免

Annales Umcs, Mathematica Pub Date : 2015-11-30 DOI:10.1515/UMCSMATH-2015-0013

Adam Gagol

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引用次数: 1

摘要

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。

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Pattern avoidance in partial words over a ternary alphabet

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.

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Annales Umcs, Mathematica

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