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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Zbl
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 
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
@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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