We extend the concept of non-decreasing Dyck paths to t-Dyck paths. We denote the set of non-decreasing t-Dyck paths by \({{\mathcal D}}_t\). Several classic questions studied in other families of lattice paths are studied here for \({{\mathcal D}}_t\). We use generating functions, recursive relations and Riordan arrays to count, for example, the following aspects: the number of non-decreasing paths in \({{\mathcal D}}_t\) with a given fixed length, the total number of prefixes of all paths in \({{\mathcal D}}_t\) of a given length, and the total number of paths in \({{\mathcal D}}_t\) with a fixed number of peaks. We give a generating function to count the number of paths in \({{\mathcal D}}_t\) that can be written as a concatenation of a given fixed number of primitive paths and we give a relation between paths in \({{\mathcal D}}_t\) and direct column-convex polyominoes.

我们将非递减 Dyck 路径的概念扩展到t -Dyck 路径。我们用\({{\mathcal D}}_t\)表示一组非递减的t -Dyck 路径。此处针对\({{\mathcal D}}_t\)研究了在其他晶格路径系列中研究的几个经典问题。我们使用生成函数、递归关系和 Riordan 数组来统计，例如以下几个方面：\({{\mathcal D}}_t\) 中给定固定长度的非递减路径的数量，在所有路径的前缀\（{{\ mathcal d}} _吨\）的给定的长度，并且路径在总数\（{{\ mathcal d}} _吨\）具有固定数量的峰值。我们给出了一个生成函数来计算\({{\mathcal D}}_t\)中路径的数量，它可以写成给定固定数量的原始路径的串联，我们给出了\({ {\mathcal D}}_t\)和直接列凸多联骨牌。