  We discuss the combinatorics of the decorated Dyck paths appearing in the
Delta conjecture framework of Haglund, Remmel and Wilson (2015) and Zabrocki
(2016), by introducing two new statistics, bounce and bounce'. We then provide
plethystic formulae for their q,t-enumerators, by proving in this way a
decorated version of Haglund's q,t-Schroeder theorem, answering a question in
Haglund, Remmel and Wilson (2015). In particular we provide both an algebraic
and a combinatorial explanation of a symmetry conjectured in Haglund, Remmel
and Wilson (2015) and Zabrocki (2016). Finally, we show a link between these
results and the q,t-square theorem of Can and Loehr (2006) (conjectured by
Loehr and Warrington (2007)), getting a new q,t-square, whose specialization at
t=1/q is identical to the classical one, and hinting to a broader phenomenon of
this type.
