= Dual Cauchy identity for symmetric functions
{title2=$\prod_{i,j}(1+x_iy_j)=\sum_\lambda s_\lambda(x)s_{\lambda'}(y)$}
= Dual Cauchy identity
{synonym}
Apply the <symmetric-function involution> in one alphabet to the ordinary <Cauchy identity>. It changes complete generators to elementary ones and, by the dual <Jacobi–Trudi identity>, sends $s_\lambda$ to $s_{\lambda'}$. This proves the identity as a formal series and relates pairings with transposed Young shapes to squarefree <matrix> weights.
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