On the Conversion of the Determinant into the Permanent

Abstract

Let Mm(F) be the vector space of m - square matrices over a field F. If X belongs to Mm(F), then xij will denote the element occuring in row i and column j of X.Let Sm be the symmetric group of degree m and ε: Sm → F the alternating character on Sm (i.e. ε(σ) = 1 or - 1 according as σ is an even or odd permutation).