2023/11/09 by Chen, Zhixing, Fei, Yumou, Gao, Jiyang +2
#05B35 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.05340
We study two-step flag positroids (P1, P2), where P1 is a quotient of P2. We provide a complete characterization of all two-step flag positroids that contain a uniform matroid, extending and completing a partial result by Benedetti, Chávez, and Jiménez. To contrast general positroids with the special case of lattice path matroids, we show that the containment relations of Grassmann necklaces and conecklaces fully characterize flag lattice path matroids, but are insufficient for general flag positroids. Additionally, we prove that the decorated permutations of any elementary quotient pair are related by a cyclic shift, resolving a conjecture of Benedetti, Chávez and Jiménez.