Polyvector fields of degree k are dual to k-forms.

Any such bundle defines a degree k + 1 cohomology class e called the Euler class of the bundle.

The function σ is homogeneous of degree k in the ξ variable.

Then we could have written a formula of degree k which is equivalent to φ, namely .

Now is a formula of degree k and therefore by assumption either refutable or satisfiable.

The k-vectors have degree k, meaning that they are sums of products of k vectors.

The k-th jet is the Taylor series of the mapping truncated at degree k and deleting the constant term.

Finally, homogeneous distributions of degree k, a negative integer, on R are all of the form:

A regular graph of degree k is connected if and only if the eigenvalue k has multiplicity one.

Differential forms of degree k are integrated over k dimensional chains.