Toward an understanding of entanglement for generalized n-qubit W-states

We solve stationarity equations of the geometric measure of entanglement for multi-qubit W-type states. In this way we compute analytically the maximal overlap of one-parameter $n$-qubit and two-parameter four-qubit W-type states and their nearest product states. Possible extensions to arbitrary W-type states and geometrical interpretations of these results are discussed in detail.