Mcalmon–Oh–Xiang's CCW-arrow characterization of positroid quotients

Let MM' and MM be positroids, and write MQMM'\trianglelefteq_Q M for the quotient relation. A CCW-arrow is the interval associated with a positroid as in the preceding definition.

Mcalmon–Oh–Xiang's conjecture. MQMM'\trianglelefteq_Q M if and only if every CCW-arrow of MM is the union of CCW-arrows of MM'.

This characterizes the quotient relation for positroids in terms of their CCW-arrows, extending the corresponding interval description for lattice path matroids. The supplied material gives no evidence that the statement has been proved or disproved.

Sources & referencesView supporting material

Primary source

Carolina Benedetti and Kolja Knauer, “Lattice path matroids and quotients”, arXiv:2202.11634 (2024).

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