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# homogeneous polynomial

A polynomial $P(x_{1},\cdots,x_{n})$ of degree $k$ is called homogeneous if $P(cx_{1},\cdots,cx_{n})=c^{{k}}P(x_{1},\cdots,x_{n})$ for all constants $c$.

An equivalent definition is that all terms of the polynomial have the same degree (i.e. $k$).

Observe that a polynomial $P$ is homogeneous iff $\deg P=\ord P$.

As an important example of homogeneous polynomials one can mention the symmetric polynomials.

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