An Extension of the Foata Map to Standard Young Tableaux
arXiv:math/0611822
Abstract
We define an inversion statistic on standard Young tableaux. We prove that this statistic has the same distribution over SYT(λ) as the major index statistic by exhibiting a bijection on SYT(λ) in the spirit of the Foata map on permutations.
15 pages, 8 figures