Multivariable Vandermonde determinants are rewritten as sums of completely factorizing Vandermonde determinants in fewer variables via amalgamated matrix determinant formulae derived from Specht module theory, yielding an elementary proof of transfinite diameter multiplicativity.
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Multivariable Vandermonde determinants, amalgams of matrices and Specht modules
Multivariable Vandermonde determinants are rewritten as sums of completely factorizing Vandermonde determinants in fewer variables via amalgamated matrix determinant formulae derived from Specht module theory, yielding an elementary proof of transfinite diameter multiplicativity.