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