The distribution of longest run lengths in integer compositions
classification
🧮 math.CO
keywords
compositionslengthsnumberpartsavoidblocksconstantcontiguous
read the original 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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