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arxiv: 1110.6779 · v2 · pith:75RFSSNEnew · submitted 2011-10-31 · 🧮 math.CO

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

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keywords numberalternatingexplicitformulapermutationsrunsdenotegiven
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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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