ok   A   contraction formula (Lemma 7.1) == definition, n <= 4 ; 285 entries  [2.5 s]
ok   B   four-point relation (8) in the exterior algebra on 8 generators  [2.5 s]
ok   B   every Rule-1 vector (9) is killed by Phi, n = 4, 5, 6 ; numbers of vectors [1, 15, 155]  [2.5 s]
ok   C   Proposition 6.1(a): M_{P,Q} = Berezin integral of Phi(P)Phi(Q) over 1..n-1, all pairs, n <= 6 ; 6844 products computed  [2.7 s]
ok   C   rank M = C_n over Q, and M restricted to non-crossing partitions is non-singular, n <= 5  [2.7 s]
ok   D   Lemma 6.4: (T(A)M)_{P,Q} = sum of w(S) over S with F_P + S + F_Q a spanning tree, n <= 3  [2.8 s]
ok   D   M symmetric; (13) T(A)M = M T(A^t)^T; (14) T(A) M T(-A)^T = (-1)^n (det A)^2 M ; (n, matrices) = [(1, 3), (2, 4), (3, 4), (4, 4), (5, 3), (6, 1)]  [3.9 s]
ok   D   bordered determinant identity (15) at 60 random integer instances  [3.9 s]
ok   D   theta_{P,Q}(r) = M_{P,Q} in (16) at random integer r, all pairs, n <= 4  [3.9 s]
ok   E   t_{P,12|34} = b_B(1)b_B(2)b_B'(3)b_B'(4) + b_B'(1)b_B'(2)b_B(3)b_B(4) for the 7 two-block P, 20 matrices  [3.9 s]
ok   E   sum_B eps_B b_B(1) b_B(2) b_{B^c}(3) b_{B^c}(4) == per A as polynomials in 16 indeterminates ; 24 monomials  [3.9 s]
ok   E   kappa T(A) = per(A) kappa at 20 integer matrices (all 15 coordinates)  [3.9 s]
ok   F   Table 1, rows n = 4, 5, 6 (exact determinants of T(A)) ; n=4: det A=137, v_p(det T(A))=14, C_n=14 | n=5: det A=47, v_p(det T(A))=42, C_n=42 | n=6: det A=251, v_p(det T(A))=132, C_n=132  [9.0 s]
ok   F   Lemma 5.2: T(I) has unit diagonal, and t_{P,Q}(I) != 0 only if Q refines P, n <= 6  [9.0 s]
TOTAL failures: 0
elapsed 9.0 s
