An n×n skew-symmetric matrix is totally positive exactly when its n(n−1)/2 selected signed minors are positive, and its Pfaffians then follow one universal sign rule.
Each path is directed from i to w−1(i) for some i ∈ [n]
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Totally positive skew-symmetric matrices
An n×n skew-symmetric matrix is totally positive exactly when its n(n−1)/2 selected signed minors are positive, and its Pfaffians then follow one universal sign rule.