A mathematical method using swap distance in permutohedrons shows crosslinguistic gestures achieve at least 77% optimality, unlikely by chance, and unifies linguistic principles under optimal assignment.
Lemma C.4(Creation or destruction of a∧-structure in two independent swaps).Consider an arrangement that has a∧-structure formed by verticest,uandvand av- erage swap distance⟨d⟩ ∧
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How to measure the optimality of word or gesture order with respect to the principle of swap distance minimization
A mathematical method using swap distance in permutohedrons shows crosslinguistic gestures achieve at least 77% optimality, unlikely by chance, and unifies linguistic principles under optimal assignment.