发表机构
Dongguk University–Seoul; Catholic Kwandong University（东国大学首尔校区; 天主教关东大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究低复杂度无限词中回文因子数量的上界，证明在因子复杂度不超过长度三分之二加一时等式成立，并构造最优性例子及局部准则。
AI 中文摘要
因子复杂度统计无限词中每个长度的不同因子数量，而回文复杂度统计在反转下不变的因子数量。对于语言在反转下封闭的递归非周期词，两个连续长度中回文因子的总数至多等于因子复杂度的一步增长加二。我们证明，当给定长度的因子复杂度不超过该长度的三分之二加一时，等式必然成立。我们构造了例子表明该界是最优的。我们还获得了一个自适应的局部准则，并将其应用于反转封闭的拟Sturmian词和回文缺陷。
英文摘要
Factor complexity counts the distinct factors of each length in an infinite word, while palindromic complexity counts those invariant under reversal. For recurrent aperiodic words with reversal-closed language, the total number of palindromic factors in two consecutive lengths is at most the one-step growth of factor complexity plus two. We prove that equality is forced whenever the factor complexity at a given length does not exceed three halves of that length plus one. We construct examples showing that the bound is optimal. We also obtain an adaptive local criterion and consequences for reversal-closed quasi-Sturmian words and palindromic defect.
Comments15 pages, 1 figure, Comments welcome!
