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

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Let M′M' and MM be positroids, and write M′⊴QMM'\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. M′⊴QMM'\trianglelefteq_Q M if and only if every CCW-arrow of MM is the union of CCW-arrows of M′M'.

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.

References

Primary source

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

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