Enumeration of unlabeled uniform hypergraphs

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	Enumeration of unlabeled uniform hypergraphs
	Qian, Jianguo ; Qian JG(钱建国)
刊名	http://dx.doi.org/10.1016/j.disc.2014.03.005
	2014-07-06
关键词	ASYMPTOTIC ENUMERATION LIMIT LAWS GRAPHS
英文摘要	NSFC [11271307]; We consider the enumeration problem of unlabeled hypergraphs by using Polya's counting theory and Burnside's counting lemma. Instead of characterizing the cycle index of the permutation group acting on the edge set epsilon, we treat each cycle in the cycle decomposition of a permutation rho acting on epsilon as an equivalence class (or transitive set) of epsilon under the operation of the group generated by rho. Compared to the cycle index-based method, our method is more effective to deal with the enumeration problem of hypergraphs. Using this method we establish an explicit counting formula for unlabeled k-uniform hypergraphs of order n, where k is an arbitrary integer with 1 <= k <= n 1. Based on our counting formula, the asymptotic behavior for the number of unlabeled uniform hypergraphs is also analyzed. (C) 2014 Elsevier B.V. All rights reserved.
语种	英语
出版者	ELSEVIER SCIENCE BV
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91317]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Qian, Jianguo,Qian JG. Enumeration of unlabeled uniform hypergraphs[J]. http://dx.doi.org/10.1016/j.disc.2014.03.005,2014.
APA	Qian, Jianguo,&钱建国.(2014).Enumeration of unlabeled uniform hypergraphs.http://dx.doi.org/10.1016/j.disc.2014.03.005.
MLA	Qian, Jianguo,et al."Enumeration of unlabeled uniform hypergraphs".http://dx.doi.org/10.1016/j.disc.2014.03.005 (2014).