Equivalence classes of Dyck paths modulo some statistics

International audienceWe investigate new equivalence relations on the set D of Dyck paths relatively to the three statistics of double rises, peaks and valleys. Two Dyck paths are -equivalent (respectively p-equivalent and v-equivalent) whenever the positions of their double rises (respectively peaks and valleys) are the same. Then, we provide generating functions for the numbers of r -, p- and -equivalence classes of D