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复杂系统与复杂性科学  2014, Vol. 11 Issue (4): 1-3    DOI: 10.13306/j.1672-3813.2014.04.001
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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a, 山石b, 史定华c
上海大学a.管理学院; b.信息研究中心; c.理学院,上海 200444
Power Law Thinking Series 4—Equivalent Condition of Heaps Law and Zipf Law
YAN Chunninga, SHAN Shib, SHI Dinghuac
a. School of Management; b. Center for Information Studies; c. School of Science, Shanghai University, Shanghai 200444, China
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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。
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阎春宁
山石
史定华
关键词 Zipf律Heaps律补分布拟幂律致密性    
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.
Key wordsZipf’s law    Heaps law    complementary distribution    quasi power-law    densification
收稿日期: 2014-04-25      出版日期: 2026-06-22
基金资助:国家自然科学基金(61174160)
通讯作者: 史定华(1941-),男,江西南昌人,学士,教授,主要研究方向为生物信息和复杂网络。   
作者简介: 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。
引用本文:   
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.
YAN Chunning, SHAN Shi, SHI Dinghua. Power Law Thinking Series 4—Equivalent Condition of Heaps Law and Zipf Law[J]. Complex Systems and Complexity Science, 2014, 11(4): 1-3.
链接本文:  
https://fzkx.qdu.edu.cn/CN/10.13306/j.1672-3813.2014.04.001      或      https://fzkx.qdu.edu.cn/CN/Y2014/V11/I4/1
[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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