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.

翻译：我们通过图表刻画了格路拟阵间的商结构。这一刻画表明，按商关系排序的格路拟阵构成一个分阶偏序集，其秩多项式的系数为纳拉亚纳数。进一步地，我们研究了全格路旗拟阵，并证明——与任意正位置旗拟阵不同——它们对应于非负旗簇中的点。该结果的基础是将强布鲁哈序的特定区间与格路旗拟阵建立对应关系。Mcalmon、Oh与Xiang近期提出的猜想给出了正位置拟阵的商结构刻画。我们利用所得结果证明了该猜想在格路拟阵情形下的成立。