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Characterizing positroid quotients of uniform matroids
Algebraic Combinatorics, Volume 9 (2026) no. 2, pp. 481-498

We study two-step flag positroids $(P_1, P_2)$, where $P_1$ is a quotient of $P_{2}$. 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. Our characterization reveals that “non-local information” is necessary for characterizing flag positroids. 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:
Accepted:
Published online:
DOI: 10.5802/alco.475
Classification: 05B35
Keywords: positroids, flag positroids, Grassmann necklaces
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Chen, Zhixing; Fei, Yumou; Gao, Jiyang; Sun, Yuxuan; Zhang, Yuchong. Characterizing positroid quotients of uniform matroids. Algebraic Combinatorics, Volume 9 (2026) no. 2, pp. 481-498. doi: 10.5802/alco.475
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     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.475/}
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