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Complete asymptotic type-token relationship for growing complex systems with inverse power-law count rankings

arXiv — cs.CL•Wednesday, November 5, 2025 at 5:00:00 AM
NeutralArtificial Intelligence

Complete asymptotic type-token relationship for growing complex systems with inverse power-law count rankings

The article titled "Complete asymptotic type-token relationship for growing complex systems with inverse power-law count rankings" examines the growth dynamics and statistical patterns observed in complex systems, with a particular focus on inverse power-law relationships exemplified by Zipf's law (F1). It discusses how these relationships appear in various finite systems, including species populations and dictionary entries, emphasizing the importance of type counts and their ranks (F3). The study supports the claim that Zipf's law applies to finite systems, reinforcing the relevance of this statistical regularity beyond idealized or infinite contexts (A1). Additionally, the article explores the type-token relationship, which relates the number of distinct types to the total number of tokens in a system, providing a comprehensive understanding of how complex systems grow and evolve over time (F2). By analyzing these patterns, the research contributes to a deeper comprehension of the underlying mechanisms governing complex systems and their emergent statistical properties.

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