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PreprintarXiv licencearXiv

Abelian maximal pattern complexity of two-dimensional words

  • Qingcheng Zeng
  • Yumei Xue
  • Cheng Zeng
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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.

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Cite

BibTeXRIS
BibTeX
@misc{zeng2026abelian,
  title = {{Abelian maximal pattern complexity of two-dimensional words}},
  author = {Qingcheng Zeng and Yumei Xue and Cheng Zeng},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.21084},
  eprint = {2608.21084},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.21084},
}
RIS
TY  - UNPB
TI  - Abelian maximal pattern complexity of two-dimensional words
AU  - Qingcheng Zeng
AU  - Yumei Xue
AU  - Cheng Zeng
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.21084
UR  - https://arxiv.org/abs/2608.21084
AB  - 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.
ER  -