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We introduce the notion of pattern in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-containment relation defines a poset structure on the set of all Dyck paths, which we call the Dyck pattern poset. Given a Dyck path P, we determine a formula for the number of Dyck paths covered by P, as well as for the number...
We study a generalization of the concept of succession rule, called jumping succession rule, where each label is allowed to produce its sons at different levels, according to the production of a fixed succession rule. By means of suitable linear algebraic methods, we obtain simple closed forms for the numerical sequences determined by such rules and give applications concerning classical combinatorial...
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