How to measure the optimality of word or gesture order with respect to the principle of swap distance minimization

arXiv:2604.01938 · cs.CL, cond-mat.stat-mech, physics.soc-ph · Submitted 2026-04-02 · Read on arXiv

cs.CL, cond-mat.stat-mech, physics.soc-ph

Submitted: 2026-04-02

Updated: 2026-09-09

Comments: Substantially rewritten. Corrections in Property B.3 and Corollary C.7

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Quadratic Assignment Problem — 8× in this paper
• Adjacency Matrix — 2× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Clustering — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Parsimony — 1× in this paper · explained in 2 episodes

Sources

• Swap distance minimization shapes the order of subject, object and verb in languages of the world

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