Question

谁来帮我翻译一下，感激不尽

The nth Catalan number is equal to the number of binary trees on n vertices, of lattice paths from (0, 0) to (2n, 0) with
steps (1, 1) and (1,−1) that stay above the y-axis (Dyck paths), and of many other objects

If b :N → Z is a function and {bi}=b(i) is the corresponding sequence, we weight a vertex of a binary tree T by bi, where i is the number of left edges on the unique path from the vertex to the root of the tree, and we define the weight w(T ) of the tree to be the product of the weights of its vertices.

感激不尽啊~~~

Answer 1

第 n 个的嘉泰罗尼亚人数字和那相等数字二进树在 n 顶点上, 格子路径从 (0,0) 到 (2 n, 0) 与
步骤 (1,1) 和 (1,?1) 那停留上方 Y轴 (Dyck 路径), 和多数其他的物体

如果 b:N-> Z 是一功能和 {bi}=b(i) 是那对应的序列, 我们重量二进的顶点树 bi 的 T, 哪里 i 是那数字左边边缘在独特的路径上从顶点到那根那树, 和我们 de?旧姓的树的重量 w(T) 是它的顶点的压重的产品。

Answer 2

太难了