The distribution of longest run lengths in integer compositions
نویسنده
چکیده
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.
منابع مشابه
Longest run of equal parts in a random integer composition
has L = 5. A composition with L = 1 is known as a Carlitz composition. The characteristics of Carlitz compositions and their generating function C〈1〉(z) (see Proposition 1) are studied in great detail in [4, 5]. The solution to the longest run problem can be broken down into four main sections. In the first section, we find a family of generating functions for integer compositions that keeps tr...
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