Equivalence classes of Dyck paths modulo some statistics

Jean-Luc Baril (1) , Armen Petrossian (1)

1 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]

We 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.

Domaines: Combinatoire [math.CO]

Jean-Luc Baril, Armen Petrossian. Equivalence classes of Dyck paths modulo some statistics. Discrete Mathematics, 2015, 338, pp.655-660. ⟨10.1016/j.disc.2014.12.003⟩. ⟨hal-01100146⟩