MinorIndex

The minor index of $p$ : the sum of the ascent positions $\sum_{p_i < p_{i+1}} i$ .

MinorIndex(p)the minor index of a one-line permutation

p

Typed signatures

Type	Package	Applies
`(list \| permutation) -> integer`	`combinatorics`	always

Domain: Permutation statistics

Details

Complementary to MajorIndex: every position is a descent or an ascent, so $\mathrm{MajorIndex}(p) + \mathrm{MinorIndex}(p) = \binom{n}{2}$
Defined over Permutation as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
Takes a Permutation, and also a bare list of integers: this reading compares entries with each other rather than with their positions, so it stands on any sequence.

Definition

Epsil, as the implementation runs it.

on Permutation, over _x

0 if Length(_x) < 2 else Sum(Filter(
                                     Range(1, Length(_x) - 1),
                                     Function(_x[i] < _x[i + 1], i),
                                   ))