de Mathématiques de Luminy
Hubert Pascal, Vuillon Laurent.
Complexity of cutting words on regular tilings.
We show that the complexity of a cutting word u in a regular tiling by a polyomino Q is equal to Pn(u) = (p+q-1)n+1,A(inverse)n > or = 0. Where Pn(u) counts the number of distinct factors of length n in the infinite word u and where the boundary of Q is constructed by 2p horizontal and 2q vertical unit segments.
Keywords: cutting words, regular tilings, complexity function, flow on the torus, combinatorics on words.