贪婪的回文长度

摘要：

在[A. Frid，S. Puzynina，L.Q. Zamboni，\textit{On palindromic factorization of words}，Adv. in Appl.Math.50（2013），737-748]中，证实了因子的回文长度有界的任何无限字最终是周期性的。我们介绍这个猜想的变种，并证明这个猜想在特定情况下。特别地，我们引入左和右贪婪回文长度。这些长度总是大于或等于初始回文长度。当一个词的前缀的贪婪左（或右）回文长度有界时，这个词最终是周期性的。

英文摘要：

In [A. Frid, S. Puzynina, L.Q. Zamboni, \textit{On palindromic factorization of words}, Adv. in Appl. Math. 50 (2013), 737-748], it was conjectured that any infinite word whose palindromic lengths of factors are bounded is ultimately periodic. We introduce variants of this conjecture and prove this conjecture in particular cases. Especially we introduce left and right greedy palindromic lengths. These lengths are always greater than or equals to the initial palindromic length. When the greedy left (or right) palindromic lengths of prefixes of a word are bounded then this word is ultimately periodic.

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