A Modular Structure Theorem for Minimal Periodic Decompositions and Periodicity of Configurations with $P_{\eta }(4,n)\le 4n$

C. F. Colle, E. Garibaldi

Nivat's conjecture asserts that every two-dimensional configuration $\eta :{\mathbb{Z}}^2\to \mathcal{A}$ whose rectangular pattern complexity satisfies $P_{\eta }(k,n)\le kn$ for some $k,…