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Cell decomposition of the positive orthogonal Grassmannian

Determine a cell decomposition for the positive orthogonal Grassmannian and identify what additional structures beyond orthopositroids are needed.

References

Determine a cell decomposition for the positive orthogonal Grassmannian. What should be added to the orthopositroids? \qquad Problem 5.4.

What is Positive Geometry? (Ranestad et al., 18 Feb 2025) in Section “Open questions”: Problem [ElMaazouz]