Forbidden substrings on weighted alphabets

In an influential 1981 paper, Guibas and Odlyzko constructed a generating function for the number of length n strings over a finite alphabet that avoid all members of a given set of forbidden substrings. Here we extend this result to the case in which the strings are weighted. This investigation was inspired by the problem of counting compositions of an integer n that avoid all compositions of a smaller integer m, a notion which arose from the consideration of one-sided random walks.Comment: 8 page

The distribution of longest run lengths in integer compositions

We find the generating function for $C(n,k,r)$, the number of compositions of $n$ into $k$ positive parts all of whose runs (contiguous blocks of constant parts) have lengths less than $r$, using recent generalizations of the method of Guibas and Odlyzko for finding the number of words that avoid a given list of subwords

Forbidden substrings on weighted alphabets

In an influential 1981 paper, Guibas and Odlyzko constructed a generating function for the number of length n strings over a finite alphabet that avoid all members of a given set of forbidden substrings. Here we extend this result to the case in which the strings are weighted. This investigation was inspired by the problem of counting compositions of an integer n that avoid all compositions of a smaller integer m, a notion which arose from the consideration of one-sided random walks.