MajorIndex

The major index of : the sum of the descent positions .

FindStatSt000004via Permutation✓↗St000330via StandardTableau↗

MajorIndex(p)the major index of a one-line permutation

Domain: Permutation statistics

Details

• Introduced by MacMahon, who proved it equidistributed with Inversions over
• Both are Mahonian, so their common generating function is the q-factorial

Examples

Implementation

referenceenginenotatio

Checked against the implementation over every permutation of 1..6.

nativeenginetypescriptpackages/collections/src/stats.ts:majorIndex

See also: Inversions, Descents, SymmetricGroup