The major index is a well-known statistic on permutations which is computed by summing the positions of descents in a permutation. Instead of considering descents, this paper investigates what happens when excedances are weighted by position in a permutation. Several theorems are presented concerning various symmetries of the resulting distribution.
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Paulukonis, Ann Marie, "Nothing in Moderation, Everything in Excess: A New Weighted Statistic on Permutations" (1994). Honors Theses, 1963-2015. 468.