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幂律思考系列文章4——论Heaps律与Zipf律等价的条件

  • 阎春宁 ,
  • 山石 ,
  • 史定华
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  • 上海大学a.管理学院; b.信息研究中心; c.理学院,上海 200444
阎春宁(1959-),女,湖北武汉人,博士,教授,主要研究方向为复杂网络和风险管理。

收稿日期: 2014-04-25

  网络出版日期: 2026-06-22

基金资助

国家自然科学基金(61174160)

Power Law Thinking Series 4—Equivalent Condition of Heaps Law and Zipf Law

  • YAN Chunning ,
  • SHAN Shi ,
  • SHI Dinghua
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  • a. School of Management; b. Center for Information Studies; c. School of Science, Shanghai University, Shanghai 200444, China

Received date: 2014-04-25

  Online published: 2026-06-22

摘要

在词频服从拟幂律分布并满足致密性的条件下,证明了Zipf律和Heaps律相互等价,并且讨论了词频序号为2时的临界行为。

本文引用格式

阎春宁 , 山石 , 史定华 . 幂律思考系列文章4——论Heaps律与Zipf律等价的条件[J]. 复杂系统与复杂性科学, 2014 , 11(4) : 1 -3 . DOI: 10.13306/j.1672-3813.2014.04.001

Abstract

In this paper, on condition that the word frequency follows the quasi power-law distribution and contents densification, it is proven that the Zipf’s law and Heaps law are equivalent, and critical behavior when γ=2 is also discussed.

参考文献

[1] Zipf G K. Human Behaviour and the Principle of Least Effort:An Introduction to Human Ecology[M]. Cambridge:Addison-Wesly, 1949.
[2] Heaps H S. Information Retrieval:Computational and Theoretical Aspects[M]. Orlando:Academic Press, 1978.
[3] Lü L Y, Zhang Z K, Zhou T. Zipf’s law leads to Heaps’ law:analyzing their relation in finite-size systems[J]. PLoS ONE, 2010, 5(12):e14139.
[4] 阎春宁,山石,史定华. 冥律思考系列文章1——论Barabási律与Pareto律互不包含[J]. 复杂系统与复杂性科学, 2014, 11(1):1-5.
Yan Chunning, Shan Shi, Shi Dinghua. Power law thinking series 1—the Barabási law and Pareto law are not mutually included[J]. Complex Systems and Complexity Science,2014,11(1):1-5.
[5] Shi D H. Theory of Network Degree Distribution[M]. Beijin:Higher Education Press, 2011.
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