P = x1**2*x2/8 + x1**2*x3/8 + x1*x2**2/8 + x1*x2*x3/4 + x1*x3**2/8 + x2**2*x3/8 + x2*x3**2/8 | degree 3 | dQ/dx_i(1) = [1, 1, 1] | symmetric
P_inf = x1**3/27 + x1**2*x2/9 + x1**2*x3/9 + x1*x2**2/9 + 2*x1*x2*x3/9 + x1*x3**2/9 + x2**3/27 + x2**2*x3/9 + x2*x3**2/9 + x3**3/27 | degree 3 | dQ/dx_i(1) = [1, 1, 1] | symmetric
chi_P(t)     = t**3 - 3*t**2 + 9*t/4 - 1/4 = (t - 1)*(4*t**2 - 8*t + 1)/4
chi_Pinf(t)  = t**3 - 3*t**2 + 2*t - 2/9
e_1(P) = 3 = sum of 1x1 permanental minors of A
e_2(P) = 9/4 = sum of 2x2 permanental minors of A
e_3(P) = 1/4 = sum of 3x3 permanental minors of A
lambda(P) = [sqrt(3)/2 + 1, 1, 1 - sqrt(3)/2] ~ [1.86602540378, 1.00000000000, 0.133974596216]
lambda(P_inf) isolating intervals (decreasing):
   [ 8284342/3951231 , 8654673/4127861 ]  ~ 2.09664836098
   [ 974569/1274346 , 1307996/1710335 ]  ~ 0.764760120093
   [ 226258/1632553 , 208263/1502711 ]  ~ 0.138591518928
g(1 - sqrt3/2) = -2/9 + sqrt(3)/8 ~ -0.00571587127611 < 0
lambda_3(P) = 1 - sqrt3/2 ~ 0.133974596216  <  lambda_3(P_inf) >= 226258/1632553 ~ 0.138591518928
partial sums k=1: 1.86602540378 <= 2.09664836098  (holds)
partial sums k=2: lambda1+lambda2 (P) = 2.86602540378444  >  (P_inf) <= 2.86140848107228  (FAILS)
total sums: both equal 3 (coefficient of t^2 is -3 in both)
CONCLUSION: lambda(P) is not majorized by lambda(P_inf); Conjecture 2 fails for P in D_{3,3}.
