Nivat's conjecture: Consider 2-dimensional words, that is, sets of letters indexed by Z². Is the following conjecture true? If the number of distinct m × n blocks is at most mn for some m and n, then the word is periodic. Recent results of Van Cyr and Bryna Kra prove the result where the bound mn is replaced by mn/2.

-- JeffreyShallit - 13 Jul 2011