The maximum Kendall-Tau distance between two permutations allowed by an acyclic constraint graph equals the number of incomparable pairs exactly when the induced poset has dimension at most 2.
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Metrics on Permutation Families Defined by a Restriction Graph
The maximum Kendall-Tau distance between two permutations allowed by an acyclic constraint graph equals the number of incomparable pairs exactly when the induced poset has dimension at most 2.