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

Published 31 Oct 2011 in math.CO | (1110.6779v2)

Abstract: 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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