This study presents a detailed investigation of bin-bin correlations in p-Pb collisions at a center-of-mass energy of \(\varvec{\sqrt{s_\textrm{NN}}}\) = 5.02 TeV using factorial correlators. The analysis examines the dependence of these correlations on pseudorapidity and event centrality, considering most-central to mid-central collision classes ( \(\varvec{0-10\%,\, 10-20\%,\, 20-30\%,\, 30-40\%,}\) and \(\varvec{40-50\%}\) ), as well as minimum-bias events. The simulated data sets are generated using the Monte Carlo-based A Multi-Phase Transport (AMPT) model (v2.26), employing configurations both with and without the string-melting mechanism. Factorial correlators are evaluated within a pseudorapidity interval of \(\varvec{\Delta \eta }\) = 12, which is subdivided into 40 and 20 bins corresponding to bin widths of \(\varvec{\delta \eta }\) = 0.3 and 0.6, respectively. The results reveal strong bin-bin correlations that increase with decreasing bin separation and exhibit no significant dependence on bin width or event centrality. Nevertheless, the observed differences are statistically robust and significant, and the overall behavior, for both string-melting and without string-melting scenarios, deviates markedly from expectations based on the log-normal approximation.
