Generalized Pascal triangle for binomial coefficients of words

Abstract

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 Sierpiński 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 describe and study the first properties of the subset of $[0,1]\times [0,1]$ associated with this extended Pascal triangle modulo a prime $p$.

20 pages, 15 figures

Cited by in corpus (1)

• Counting the number of non-zero coefficients in rows of generalized Pascal triangles