Nivat's Conjecture and Pattern Complexity in Algebraic Subshifts

06/19/2018
by   Jarkko Kari, et al.
0

We study Nivat's conjecture on algebraic subshifts and prove that in some of them every low complexity configuration is periodic. This is the case in the Ledrappier subshift (the 3-dot system) and, more generally, in all two-dimensional algebraic subshifts over F_p defined by a polynomial without line polynomial factors in more than one direction. We also find an algebraic subshift that is defined by a product of two line polynomials that has this property (the 4-dot system) and another one that does not.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset