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.â€¦ (More)

This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomial coefficients ofâ€¦ (More)

Many digital functions studied in the literature, e.g., the summatory function of the base-k sum-of-digits function, have a behavior showing some periodic fluctuation. Such functions are usuallyâ€¦ (More)

We count the number of distinct (scattered) subwords occurring in the base-b expansion of the nonnegative integers. More precisely, we consider the sequence (Sb(n))nâ‰¥0 counting the number of positiveâ€¦ (More)

The Chen-Fox-Lyndon theorem states that every finite word over a fixed alphabet can be uniquely factorized as a lexicographically nonincreasing sequence of Lyndon words. This theorem can be used toâ€¦ (More)