Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Zeng, Qingcheng, Xue, Yumei, Zeng, Cheng
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204116881