If G is a group generated by two 2x2 matrices A and B having determinant +1, with entries from the complex field C, it is known that the trace of any word in A and B, W(A, B) is a polynomial with integral coefficients in the three variables: x = traced), >> = trace(fi), z -tracers), defined as trace W(A, B) = P(x,y, z), where P is determined uniquely by the conjugacy class of W (A, B) . The actual computation of this trace polynomial is not easily obtained. It is the purpose of this paper to

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... ive an explicit formula for this trace polynomial, and to indicate some consequences of it.