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arXiv · 0906.5196

The distribution of longest run lengths in integer compositions

Herbert S. Wilf
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Abstract

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.

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Herbert S. Wilf. 2009-06-29. The distribution of longest run lengths in integer compositions. https://arxiv.org/abs/0906.5196

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