论文标题
晶格路径矩形和商
Lattice path matroids and quotients
论文作者
论文摘要
我们根据图表的图表来表征晶格路径矩阵（LPM）之间的商。这种表征使我们能够表明，用商订购LPM会产生一个分级的poset，其等级多项式具有Narayana数字作为系数。 此外，我们研究了完整的晶格路径标志矩形，并表明 - 与任意阳性标志矩阵相反，它们对应于非负标志品种中的点。在此结果的基础上，用晶格路径标志矩阵鉴定了强bruhat顺序的某些间隔。 麦卡蒙（McAlmon），OH和Xiang最近的一个猜想陈述了源自质体的商的特征。在LPM的情况下，我们使用结果证明了这种猜想。
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.
