  We present several formulas for the traces of elements in complex hyperbolic
triangle groups generated by complex reflections.
  The space of such groups of fixed signature is of real dimension one. We
parameterise this space by a real invariant alpha of triangles in the complex
hyperbolic plane. The main result of the paper is a formula, which expresses
the trace of an element of the group as a Laurent polynomial in exp(i alpha)
with coefficients independent of alpha and computable using a certain
combinatorial winding number. We also give a recursion formula for these
Laurent polynomials and generalise the trace formulas for the groups generated
by complex mu-reflections.
  We apply these formulas to prove some discreteness and some non-discreteness
results for complex hyperbolic triangle groups.
