Geodesic
The distribution of run lengths in integer compositions
The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2
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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.
DOI : 10.37236/2019
Classification : 05A15, 05A19, 68R15
Mots-clés : generating function, number of compositions, avoiding words, forbidden words, Carlitz composition 
@article{10_37236_2019,
     author = {Herbert S. Wilf},
     title = {The distribution of run lengths in integer compositions},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {2},
     doi = {10.37236/2019},
     zbl = {1236.05014},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2019/}
}
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Herbert S. Wilf. The distribution of run lengths in integer compositions. The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2. doi: 10.37236/2019

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