  The aim of this paper is to make sample computations with the Salvetti
complex of the "center of mass" arrangement introduced in [arXiv:math/0611732]
by Cohen and Kamiyama. We compute the homology of the Salvetti complex of these
arrangements with coefficients in the sign representation of symmetric groups
on F_p in the case of four particles. We show, when p is an odd prime, the
homology is isomorphic to the homology of the configuration space F(C,4) of
distinct four points in the complex plane with the same coefficients. When p=2,
we show the homology is different from that of F(C,4), hence obtain an
alternative and more direct proof of a theorem of Cohen and Kamiyama in
[arXiv:math/0611732].
