We introduce a notion of Dyck paths with coloured ascents. For several ways of colouring, when the set of colours is itself some class of lattice paths, we establish bijections be...
In a previous work [26], by considering paths that are partially weighted, the generating function of Dyck paths was shown to possess a type of symmetry, called an exchange relati...
Given a sequence of integers b = (b0,b1,b2,...) one gives a Dyck path P of length 2n the weight wt(P) = bh1 bh2 ···bhn , where hi is the height of the ith ascent of P. The corr...