MajorIndex on DyckPath

The sum of the descent positions of the step word — where an up step is followed by a down step.

Same name as the permutation statistic, genuinely a different function — which is why definitions are keyed by signature.

Called as CombinatorialStat(x, "MajorIndex"). The head's page has its examples.

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The same name on other carriers, each its own implementation: Permutation, IntegerComposition, BinaryWord.