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

Lattice path matroids and quotients