AI 中文总结
该研究引入对应带彩色步格路行走的新型Riordan矩阵，推导其相关公式，得到格路行走中任意模式出现次数的显式组合公式，并建立该矩阵与格的Whitney数的联系。
AI 中文摘要
我们引入一类对应带彩色步的格路行走的新型Riordan矩阵，证明该类矩阵对应一类伪对合，进而求出这类Riordan矩阵元素的生成函数与显式组合公式；利用这些Riordan矩阵，得到格路行走中任意模式出现次数的显式组合公式；最后，在格路行走上定义一个分配格，并将新型RNA矩阵与格的Whitney数建立联系。
英文摘要
We introduce a new class of Riordan matrices corresponding to lattice walks with colored steps. We show that this class corresponds to a class of pseudo-involutions and then find both generating functions and explicit combinatorial formulas for entries of these Riordan matrices. We use these Riordan matrices to find an explicit combinatorial formula for the occurences of an arbitrary pattern in our lattice walks. Finally, we define a distributive lattice on our lattice walks and connect our new RNA matrices to Whitney numbers of lattices.
