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A Note About the Conjecture on Spearman's Rho and Kendall's Tau

In this paper, we consider the open question on Spearman's rho and Kendall's tau of Nelsen [1991]. Using a technical hypothesis, we can answer in the positive. One question remains open: how can we understand the technical hypothesis? Because this hypothesis is not right in general, we could find some pathological cases which contradict Nelsen's conjecture.