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Counting permutations by their runs up and down

E. Rodney Canfield·Herbert S. Wilf
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Abstract

We find a formula for the number of permutations of $[n]$ that have exactly $s$ runs up and down. The formula is at once terminating, asymptotic, and exact.

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E. Rodney Canfield, Herbert S. Wilf. 2006-09-25. Counting permutations by their runs up and down. https://arxiv.org/abs/math/0609704

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