Let F be any field and let P = spanp{o(1) To (2) Lo(n) | ...

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Let F be any field and let P₁ = spanp{o(1) To (2) Lo(n) | σ € S₂} be the vector space of multilinear polynomials in the non commutative variables 1,...,. Consider the vector subspace W = span{(wwwwwwww submonomials of some o(1)(2)(n) 4 eventually empty) C Pn. Prove that dim Pn/W Sn. Let F be any field and let P₁ = spanp{o(1) To (2) Lo(n) | σ € S₂} be the vector space of multilinear polynomials in the non commutative variables 1,...,. Consider the vector subspace W = span{(wwwwwwww submonomials of some o(1)(2)(n) 4 eventually empty) C Pn. Prove that dim Pn/W Sn.

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Let S be the set of all permutations of 12n Let P be the vector space of multilinear polynomials in ... View the full answer