The index of a permutation 
is defined as the sum of all subscripts 
such that 
, for 
. MacMahon (1960) proved that the number of permutations
of size 
having index 
is the same as the number having exactly 
inversions (Skiena 1990, p. 29). The permutation index
can be computed as Index[p]
in the Wolfram Language package Combinatorica`
.
Permutation Index
See also
PermutationExplore with Wolfram|Alpha
References
Knuth, D. E. The Art of Computer Programming, Vol. 3: Sorting and Searching, 2nd ed. Reading, MA: Addison-Wesley, 1998.MacMahon, P. A. Combinatory Analysis, 2 vols. New York: Chelsea, 1960.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.Referenced on Wolfram|Alpha
Permutation IndexCite this as:
Weisstein, Eric W. "Permutation Index." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PermutationIndex.html