In order to ensure that the latter describe a partial injective function, we enforce the following constraints: We can now write Equation (1) in terms of the variables x ij (which capture exactly the same information as the function σ): Note that Equations (1) and (5) are summations of the same terms.
4 Equation (5) is not linear in the variables x ij as it contains products of the form x ij x kl .