Geodesic
Statistics for 3-letter patterns with repetitions in compositions
Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 3.

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A composition $\pi = \pi_1 \pi_2 \cdots \pi_m$ of a positive integer $n$ is an ordered collection of one or more positive integers whose sum is $n$. The number of summands, namely $m$, is called the number of parts of $\pi$. Using linear algebra, we determine formulas for generating functions that count compositions of $n$ with $m$ parts, according to the number of occurrences of the subword pattern $\tau$, and according to the sum, over all occurrences of $\tau$, of the first integers in their respective occurrences, where $\tau$ is any pattern of length three with exactly 2 distinct letters. 
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     author = {Shabani, Armend and Gjergji, Rexhep},
     title = {Statistics for 3-letter patterns with repetitions in compositions},
     journal = {Discrete mathematics & theoretical computer science},
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     year = {2015-2016},
     doi = {10.46298/dmtcs.2156},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2156/}
}
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Shabani, Armend; Gjergji, Rexhep. Statistics for 3-letter patterns with repetitions in compositions. Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 3. doi : 10.46298/dmtcs.2156. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2156/

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