  We study the crossover behavior of the Hall resistance between the integer
quantum Hall regime and a regime dominated by the Aharonov-Bohm oscillations,
in a system of 4-probe quantum dot with an artificial impurity confined inside.
In a previous study [M. Lei, N.J. Zhu and Hong Guo, Phys. Rev. B. 52, 16784,
(1995)], a peculiar set of symmetry relations between various scattering
probabilities were found in this crossover regime. In this paper we examine the
universality of this set of symmetry relations using different shapes of the
quantum dot and positions of the artificial impurity. The symmetry holds for
these changes and we conclude that in this transport regime the general
behavior of the Hall resistance is determined by the competition of the quantum
Hall and Aharonov-Bohm effects, rather than by the detailed shapes of the
structure.
