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.
