Major index

This is a statistic on permutations. Given some $w \in S_{n}$ , define

maj (w) = \sum_{i descent} i

the sum of the indices of all the descents.

Examples

$w = 2, 5, 7, 3, 1, 6, 8, 4$
$maj (w) = 3 + 4 + 7 = 14$