Calculation of amplitude with n=5, k=3 using the book by Arkani-Hamed et al

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This is a pretty technical question so before I post all the details, let me first ask if someone might be able to help.

I am going over the book Grassmannian Geometry of Scattering Amplitudes and I am trying to calculate the anti MHV amplitude with five particles, at tree level (or, equivalently, the NHMV). The answer if the three particles of negative helicities are the first three, should be [tex] \frac{[45]^4}{[12][23][34][45][51] } [/tex] (all that times the usual four momentum delta function, of course).

I have tried to get this using an approach similar to what they do on page 90 to obtain the amplitude for n=6,k=3. I have a matrix in the style of to their matrix in Eq.(8.6) which obeys all the condition imposed by the delta functions. However, when I plug that into the formula (8.4) to get the amplitude and I do some manipulations, I end up with almost the correct expression, the only problem is that I have an extra factor of [itex] \langle 2 4 \rangle [/itex] in the denominator. I get a factor of [itex] \langle 2 4 \rangle [/itex] for each of the five minors appearing in the denominator and I get a factor of [itex] \langle 2 4 \rangle^4 [/itex] from the integration over the Grassmann variables when choosing the first three particles to have [itex]h=-1[/itex].

I will provide more details if someone knows a bit about this topic. This is driving me crazy since it should be straightforward. There is obviously something very simple that I am completely missing.
 
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