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The first ascent of size $d$ or more in compositions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006) Cet article a éte moissonné depuis la source Episciences

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A composition of a positive integer $n$ is a finite sequence of positive integers $a_1, a_2, \ldots, a_k$ such that $a_1+a_2+ \cdots +a_k=n$. Let $d$ be a fixed nonnegative integer. We say that we have an ascent of size $d$ or more at position $i$, if $a_{i+1}\geq a_i+d$. We study the average position, initial height and end height of the first ascent of size $d$ or more in compositions of $n$ as $n \to \infty$. 
@article{DMTCS_2006_special_252_a33,
     author = {Brennan, Charlotte and Knopfmacher, Arnold},
     title = {The first ascent of size $d$ or more in compositions},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2006},
     volume = {DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities},
     doi = {10.46298/dmtcs.3509},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3509/}
}
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Brennan, Charlotte; Knopfmacher, Arnold. The first ascent of size $d$ or more in compositions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006). doi: 10.46298/dmtcs.3509

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