Given polynomial P(a,b,c,d,e,f........n) = (a^0)(b^1)(c^2).......(n^n)(adsbygoogle = window.adsbygoogle || []).push({});

show that the sum of P(a,b,c,d,e,f........x) when acted upon by the symmetric group of order n and each time multipled by the sgn function (1 if even and -1 if odd); that this sum is equal to the vandermonde determinant of these variables. Any insights? I'm quite lost.

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# I'm stuck on a proof that's probably trivial, any insights?

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