二维词的阿贝尔极大模式复杂度
Abelian maximal pattern complexity of two-dimensional words
浏览论文内容
中文总结 AI 辅助
本文研究二维词在阿贝尔等价下的极大模式复杂度，针对非投影双周期的二维词建立其阿贝尔极大模式复杂度的下界并证明其紧性，进而得到强回归二元非双周期词的精确复杂度与双周期性的有界性准则。
中文摘要 AI 辅助
本文研究二维词在阿贝尔等价下的极大模式复杂度。针对非投影双周期的二维词，在存在横向回归方向或强回归的条件下，我们建立了其阿贝尔极大模式复杂度的下界，进一步证明该下界是紧的。由此，我们得到强回归二元非双周期词的精确复杂度，以及双周期性的有界性准则。
英文摘要
In this paper, we study the maximal pattern complexity of two-dimensional words up to Abelian equivalence. We establish a lower bound for the Abelian maximal pattern complexity of two-dimensional words that are non-doubly periodic by projection under the existence of a transverse recurrence direction or strong recurrence. We further show that the bound is attained for every alphabet size. As a consequence, we characterize double periodicity of strongly recurrent binary words by the boundedness of their Abelian maximal pattern complexity.
发表机构
- School of Mathematical Sciences, Beihang University（北京航空航天大学数学科学学院）
- School of Mathematics and Information Science, Shandong Technology and Business University（山东工商学院数学与信息科学学院）
机构由 AI 辅助整理，请以论文原文为准。
