The Distribution of Run Lengths in Integer Compositions

Herbert S. Wilf

Abstract


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.


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