This topic is such a hard one. I just learned tha 7:43 t it is the Vandermonde Polynomial. Now I dont know if the polynomial is used for algebric expansion or just signed permutaion of the original polynomial. Besdes why exactly are we using polynomial to express Permutaion Groups. Granted we only want to find out whether a given permuatiaon is an even or an odd permutaion of some original permutaions, how is that we get a positive Vandermond sign for even permuation. and -ve Vandermonde sign for Odd permuations. Going back to square one again - what is the original permuation before the identity permutaion? As mentioned in the video some other time we had ceratin set of distinct symbols. The symmetric group repersents list of all permuations of the symbols , thus its elements are the Set permuations and here we do care about their order.
