Counting permutations by their runs up and down

Details Counting permutations by their runs up and down Counting permutations by their runs up and down

2006-09-25

arxiv.org/abs/math/0609704v1

Mathematics

Combinatorics

12 pages

Scientific paper

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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