Complete Homogeneous Symmetric Polynomial - Examples

Examples

The following lists the basic (as explained below) complete homogeneous symmetric polynomials for the first three positive values of n.

For n = 1:

For n = 2:

\begin{align} h_1(X_1,X_2)&= X_1 + X_2\\ h_2(X_1,X_2)&= X_1^2 + X_1X_2 + X_2^2. \end{align}

For n = 3:

\begin{align} h_1(X_1,X_2,X_3) &= X_1 + X_2 + X_3\\ h_2(X_1,X_2,X_3) &= X_1^2 + X_2^2 + X_3^2 + X_1X_2 + X_1X_3 + X_2X_3\\ h_3(X_1,X_2,X_3) &= X_1^3+X_2^3+X_3^3 + X_1^2X_2+X_1^2X_3+X_2^2X_1+X_2^2X_3+X_3^2X_1+X_3^2X_2 + X_1X_2X_3. \end{align}

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