We introduce a new poset structure on Dyck paths where the covering relation is a particular case of the relation inducing the Tamari lattice. We prove that the transitive closure of this relation endows Dyck paths with a lattice structure. We provide a trivariate generating function counting the number of Dyck paths with respect to the semilength, the numbers of outgoing and incoming edges in the Hasse diagram. We deduce the numbers of coverings, meet and join irreducible elements. As a byproduct, we present a new involution on Dyck paths that transports the bistatistic of the numbers of outgoing and incoming edges into its reverse. Finally, we give a generating function for the number of intervals, and we compare this number with the number of intervals in the Tamari lattice.

翻译：我们在Dyck路径上引入一种新的偏序结构，其中覆盖关系是诱导Tamari格关系的一个特例。我们证明该关系的传递闭包赋予Dyck路径一种格结构。我们给出一个三变量生成函数，根据半长、Hasse图中出边与入边的数量计数Dyck路径的数目，由此推导出覆盖元、不可约交元与不可约并元的数量。作为副产品，我们提出一种新的Dyck路径对合，该对合将出边与入边数量的双统计量转换为其反向统计量。最后，我们给出区间数量的生成函数，并将该数量与Tamari格中的区间数量进行比较。