The Distribution of Run Lengths in Integer Compositions

We find explicitly the generating function for the number of compositions of $n$ that avoid all words on a given list of forbidden subwords, in the case where the forbidden words are pairwise letter-disjoint. From this we get the gf for compositions of $n$ with no $k$ consecutive parts equal, as wel...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2011-10, Vol.18 (2)
Main Author: Wilf, Herbert S.
Format: Article
Language:English
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Summary:We find explicitly the generating function for the number of compositions of $n$ that avoid all words on a given list of forbidden subwords, in the case where the forbidden words are pairwise letter-disjoint. From this we get the gf for compositions of $n$ with no $k$ consecutive parts equal, as well as the number with $m$ parts and no consecutive $k$ parts being equal, which generalizes corresponding results for Carlitz compositions.
ISSN:1077-8926
1077-8926
DOI:10.37236/2019