An explicit formula for the number of permutations with a given number of alternating runs

Details An explicit formula for the number of permutations with a given number of alternating runs An explicit formula for the number of permutations with a given number of alternating runs

2011-10-31

arxiv.org/abs/1110.6779v2

Mathematics

Combinatorics

6 pages

Scientific paper

Let $R(n,k)$ denote the number of permutations of ${1,2,...,n}$ with $k$
alternating runs. In this note we present an explicit formula for the numbers
$R(n,k)$.

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