标题： 加权Dyck路径与避免1234的上升下降排列之间的双射 显示英文标题

标题： A Bijection Between Weighted Dyck Paths and 1234-avoiding Up-Down Permutations

摘要： 三维Catalan数是经典（二维）Catalan数的一种变体，它们计数了诸多有趣的对象，其中包括形状为(n,n,n)的标准Young表。 在本文中，我们介绍了两种三维Catalan对象之间的结构双射： 避免1234的上下排列，以及一类加权Dyck路径。 显示英文摘要

摘要： Three-dimensional Catalan numbers are a variant of the classical (bidimensional) Catalan numbers, that count, among other interesting objects, the standard Young tableaux of shape (n,n,n). In this paper, we present a structural bijection between two three-dimensional Catalan objects: 1234-avoiding up-down permutations, and a class of weighted Dyck paths.