Séminaire Lotharingien de Combinatoire, 93B.109 (2025), 12 pp.

Zhixing Chen, Yumou Fei, Jiyang Gao, Yuxuan Sun and Yuchong Zhang

Partial Flag Positroids

Abstract. 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.

Received: November 15, 2024. Accepted: February 15, 2025. Final version: April 1, 2025.

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