q, p-Analogue des nombres de Catalan Original Research Article

We propose to study the q, p-Catalan numbers Cn(q, p) defined through the recurrence Cn(q, p) = Cn−1(q, p) + ∑k=0k−n−2 qpk Ck(q, p)Cn−1−k(q, p) (C0(q, p) = C1(q, p) = 1). We also give new combinatorial interpretations of Carlitzʹs q-Catalan numbers that is the case p = q2.