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Descents ​

The number of descents of : positions with .

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Descents(p)the descent count of a one-line permutation

Domain: Permutation statistics

Details
  • The permutations of with descents are counted by the Eulerian number
  • Complementary to Ascents: every adjacent pair is one or the other, so

Examples

See also: Ascents, MajorIndex, SymmetricGroup