By a theorem of A'Campo, the eigenvalues of certain Coxeter transformations
are positive real or lie on the unit circle. By optimally bounding the
signature of tree-like positive Hopf plumbings from below by the genus, we
prove that at least two thirds of them lie on the unit circle. In contrast, we
show that for divide links, the signature cannot be linearly bounded from below
by the genus.Comment: 16 pages, 5 figures, with appendix by Peter Feller and Livio Liecht
