On a conjecture on bidimensional words

Chiara Epifanio, Michel Koskas, Filippo Mignosi
2003 Theoretical Computer Science  
We prove that, given a double sequence w over the alphabet A (i.e. a mapping from Z 2 to A), if there exists a pair (n0; m0) ∈ Z 2 such that pw(n0; m0) ¡ 1 100 n0m0, then w has a periodicity vector, where pw is the complexity function in rectangles of w.
doi:10.1016/s0304-3975(01)00386-3 fatcat:63tdrfolxrbrhob4lokvsjiiza