The major index of a permutation is the sum of its permutation descent positions:It uses positions, rather than the values being compared. For , the permutation descents occur at positions one and three, giving , whereas the descent number is two.
The major index has the same distribution over all permutations of elements as the inversion number:For , the six values give . Individual statistics need not agree: has major index one and two inversions. The shared generating polynomial is a statement about their distribution across the whole symmetric group.[ref]
Enumerative Combinatorics, Volume 1 (second-edition draft) by Richard Stanley. sections 1.3–1.4, inversions and major index
Articles by others on the same topic
A major index typically refers to a stock market index that represents a significant portion of the market and is widely used as a benchmark to gauge the overall performance of the market or specific sectors of the economy. Major indices consist of a select group of stocks that are meant to reflect the broader market's behavior and trends. Some of the most well-known major indices include: 1. **S&P 500**: Comprises 500 of the largest U.S.