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：我们引入了一种新的Dyck路径偏序集结构，其覆盖关系是诱导Tamari格关系的特例。我们证明该关系的传递闭包赋予Dyck路径一个格结构。我们给出了一个三变量生成函数，用于统计Dyck路径的半长、哈斯图中出边和入边的数量。由此推导出覆盖关系、交不可约元与并不可约元的计数。作为推论，我们提出了一种新的Dyck路径对合变换，该变换将出边与入边的双统计量映射为其逆序统计量。最后，我们给出了区间数的生成函数，并将该数量与Tamari格中的区间数进行了比较。