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

Decorated Dyck paths, the Delta conjecture, and a new q,t-square