  We are motivated by tripartite entanglement for fermions. While GHZ or W
states involve 3-fold intrication, we consider here piecewise intrication of 3
fermions in ${\bf C}^2$, namely of type $ab+bc+ca$. Before interaction with
Stern-Gerlach apparatus, qu-bits are distinguishable; at the output however
they turn into un-distinguishable particles, whose anti-symmetric wave function
is of the form $\det(b-a,c-a)$ (affine determinant). More generally, $d+1$
intricated fermions in ${\bf C}^d$ can be represented by the anti-symmetric
wave function $\det(a_1-a_0,a_2-a_0,\cdots,a_d-a_0)$. We investigate also
properties of affine Slater determinants, as expectation values or reduced
density matrices.
