Initial partonic eccentricities in Au+Au collisions at center-of-mass energy $sqrt{s_{NN}}$ = 200 GeV are investigated using a multi-phase transport model with string melting scenario. The initial eccentricities in different order of harmonics are studied using participant and cumulant definitions. Eccentricity in terms of second-, fourth- and sixth order cumulants as a function of number of participant nucleons are compared systematically with the traditional participant definition. The ratio of the cumulant eccentricities $varepsilonleft{4right}/varepsilonleft{2right}$ and $varepsilonleft{6right}/varepsilonleft{4right}$ are studied in comparison with the ratio of the corresponding flow harmonics. The conversion coefficients ($v_n/varepsilon_n$) are explored up to fourth order harmonic based on cumulant method. Furthermore, studies on transverse momentum ($p_T$) and pseudo-rapidity ($eta$) dependencies of eccentricities and their fluctuations are presented. As in ideal hydrodynamics initial eccentricities are expected to be closely related to the final flow harmonics in relativistic heavy-ion collisions, studies of the fluctuating initial condition in the AMPT model will shed light on the tomography properties of the initial source geometry.
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