  Twisted Alexander invariants of knots are well-defined up to multiplication
of units. We get rid of this multiplicative ambiguity via a combinatorial
method and define normalized twisted Alexander invariants. We then show that
the invariants coincide with sign-determined Reidemeister torsion in a
normalized setting, and refine the duality theorem. We further obtain necessary
conditions on the invariants for a knot to be fibered, and study behavior of
the highest degrees of the invariants.
