Des triangles de Pascal généralisés aux coefficients binomiaux de mots finis

We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpinski gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we show the existence of a subset of [0, 1]×[0, 1] associated with this extended Pascal triangle modulo a prime p.