Cyclic descents for Motzkin paths

A notion of cyclic descents on standard Young tableaux (SYT) rectangular shape was introduced by Rhoades, and extended to certain skew shapes Adin, Elizalde Roichman. The descent set restricts the usual when largest value is ignored, has property that number SYT a given with D invariant under shifts entries D. Reiner Roichman proved map if only it not connected ribbon. Unfortunately, their proof nonconstructive. Recently Huang constructed an explicit for all where this possible. In earlier version Roichman's paper, they asked find statistics combinatorial objects which are equidistributed shapes. we explicitly describe sets Motzkin paths, three-row Moreover, in light Stanley's shuffling theorem, give bijective paths.