Simultaneous Maj Statistics

Fix-Mahonian Calculus, II: Further statistics

Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistributed either with the triplet (fix,des,maj), or the pair (fix,maj), where " fix, " " des " and " maj " denote the number of fixed points, the number of descents and the major index, respectively.

Fix-Mahonian calculus, I: Two transformations

We construct two bijections of the symmetric group Sn onto itself that enable us to show that three new three-variable statistics are equidistributed with classical statistics involving the number of fixed points. The first one is equidistributed with the triplet (fix, des,maj), the last two with (fix, exc,maj), where “fix,” “des,” “exc” and “maj” denote the number of fixed points, the number o...

Simultaneous optic neuropathy and osmotic demyelinating syndrome in hyperemesis gravidarum.

Dominique Foata

Using classical transformations on the symmetric group and two transformations constructed in Fix-Mahonian Calculus I, we show that several multivariable statistics are equidistributed either with the triplet (fix,des,maj), or the pair (fix,maj), where " fix, " " des " and " maj " denote the number of fixed points, the number of descents and the major index, respectively.

Two Statistics Linking Dyck Paths and Non-crossing Partitions

We introduce a pair of statistics, maj and sh, on Dyck paths and show that they are equidistributed. Then we prove that this maj is equivalent to the statistics ls and rb on non-crossing partitions. Based on non-crossing partitions, we give the most obvious q-analogue of the Narayana numbers and the Catalan numbers.