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Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (1) :127-130    DOI: 10.1007/s10255-012-0128-8
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Erdos-Ko-Rado Theorems of Labeled Sets
Xing-bo GENG1, Yu-shuang LI2
1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
2. School of Science, Yanshan University, Qinhuangdao 066004, China
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Abstract For k = (k1, … , kn) ∈ Nn, 1 ≤ k1 ≤ … ≤ kn, let Lkr be the family of labeled r-sets on k given by Lkr := {{(a1, la1), … , (ar, lar)} : {a1, … , ar} ⊆ [n], lai ∈ [kai], i = 1, … , r}. A family A of labeled r-sets is intersecting if any two sets in A intersect. In this paper we give the sizes and structures of intersecting families of labeled r-sets.  
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KeywordsErdos-Ko-Rado theorem   labeled set   intersecting family     
Abstract: For k = (k1, … , kn) ∈ Nn, 1 ≤ k1 ≤ … ≤ kn, let Lkr be the family of labeled r-sets on k given by Lkr := {{(a1, la1), … , (ar, lar)} : {a1, … , ar} ⊆ [n], lai ∈ [kai], i = 1, … , r}. A family A of labeled r-sets is intersecting if any two sets in A intersect. In this paper we give the sizes and structures of intersecting families of labeled r-sets.  
KeywordsErdos-Ko-Rado theorem,   labeled set,   intersecting family     
Received: 2009-11-07;
Fund:

Supported by the National Natural Science Foundation of China (No. 11001249) and the Mathematical Tianyuan Foundation of China (No. 11026180).

Cite this article:   
.Erdos-Ko-Rado Theorems of Labeled Sets[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2012,V28(1): 127-130
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-012-0128-8      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2012/V28/I1/127
 
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