A permutation descent is an index with such that in a permutation (NIST DLMF, §26.14(i)). For example, has a single descent, at index 1. The opposite strict inequality defines a permutation ascent.

The Eulerian number counts permutations of elements with exactly descents. It also counts those with ascents, since replacing every entry by exchanges the two statistics.

See also

Eulerian Number, Permutation, Permutation Ascent

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References

NIST Digital Library of Mathematical Functions. "Permutations: Order Notation." §26.14(i). https://dlmf.nist.gov/26.14(i).

Cite this as:

Weisstein, Eric W. "Permutation Descent." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PermutationDescent.html

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