The number of elements greater than 
to the left of 
in a permutation gives the
th element of the inversion vector (Skiena
1990, p. 27).
Inversion Vector
See also
Permutation InversionExplore with Wolfram|Alpha
References
Skiena, S. "Inversion Vectors." §1.3.1 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 27-28, 1990.Thompkins, C. B. Machine Attacks on Problems Whose Variables are Permutations. Providence, RI: Amer. Math. Soc., p. 203, 1956.Referenced on Wolfram|Alpha
Inversion VectorCite this as:
Weisstein, Eric W. "Inversion Vector." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InversionVector.html