We characterize the quotients among lattice path matroids (LPMs) in terms of their diagrams. This characterization allows us to show that ordering LPMs by quotients yields a graded poset, whose rank polynomial has the Narayana numbers as coefficients. Furthermore, we study full lattice path flag matroids and show that—contrary to arbitrary positroid flag matroids—they correspond to points in the nonnegative flag variety. At the basis of this result lies an identification of certain intervals of the strong Bruhat order with lattice path flag matroids. A recent conjecture of Mcalmon, Oh, and Xiang states a characterization of quotients of positroids. We use our results to prove this conjecture in the case of LPMs.

我们用图来描述格子路径拟阵 (LPM) 之间的商。这种表征使我们能够证明，按商对 LPM 进行排序会产生分级偏序集，其秩多项式以 Narayana 数作为系数。此外，我们研究了全格路径标志拟阵，并表明与任意正似标志拟阵相反，它们对应于非负标志簇中的点。在此结果的基础上，用格子路径旗形拟阵识别了强 Bruhat 阶的某些区间。麦卡蒙、吴和翔最近的一个猜想阐述了正类商的特征。我们用我们的结果在 LPM 的情况下证明了这个猜想。