Erdos, 柯召,Rado证明了下面的定理: Theorem 1(Erdos-Ko-Rado): 设 n≥2k,那么[n] 的k元子集构成的相交系的规模至多只能是 (n−1k−1) . Remark: 进一步可以证明, 相交系取到这个最大规模时当且仅当这个相交系是个Star, 即所有相交系中的集合都包含某个固定的数 x . 我们下面用两种方法(概率方法...
Erdos–Ko–Rado theoremAntipodal vectors{ 0 , ± 1 } -vectorsIntersecting familyThe main object of this paper is to determine the maximum number of {0,±1} { 0 , ± 1 } mathContainer Loading Mathjax -vectors subject to the following condition. All vectors have length n , exactly k of...
NowweintroducethefullErd˝os–Ko–Radotheorem,whichwasconjecturedby Franklin[4],andprovedbyAhlswedeandKhachatrianin[1].Set AK(n,k,t,r):=|{B∈ [n] k :|B∩[t+2r]|≥t+r}|. Theorem1([1])Let1≤t≤k≤nandB⊂ [n] k bet-intersecting.If (k−t+1)(2+ t−1 r+1 )≤n...
EKR theorem 0 引言 极值 问题是 代数 学 的重 要研究 课题 之一 ,也是组合学 中一个 重要 的研 究分支 ,其 内容 相当 丰富 _】 多年 来 ,极值 问题 一直 备 受许 多国 内外 学者 的关 注与 探究,EKR 定理 正 是组 合 极值 理论 中著 名 的定 理.EKR定 理是 Erd6s,Ko和 Rado提 出的 ,...
ofErd6s—Ko-RadoTheorem.TheseconddevotestotheNMprop— erty andtheLYM property of intersecting antichains。Inamore generalsetting wegive a unifiedtreatmentoftheSperner-typepropertiesandtheintersectingpropertyinaranked poset。Then,the LYM property and
Thus, this problem may be seen as an extension of the classical Erds–Ko–Rado theorem. Rather surprisingly there is a phase transition in the behaviour of the maximum at n=k 2 n = k 2 mathContainer Loading Mathjax . Nevertheless, our solution is complete. The main tools are from ...
机译:用于有限染色条件的Erdos-Ko-rado定理 摘要 In [W. N. Hsieh, Intersection theorems for finite vector spaces, Discrete Math. 12 (1975) 1-16], Hsieh obtained the Erdos-Ko-Rado theorem for finite vector spaces. This paper generalizes Hsieh's result and obtains the Erdos-Ko-Rado theorem ...
On the other, many of the topics considered can be regarded as analogues for sets of permutations of results on set-systems (or hypergraphs) springing from the Erdos--Ko--Rado theorem. I begin with the celebrated Orbit-Counting ... PJ Cameron 被引量: 1发表: 1999年 On Erdos-Ko-Rado for...
3) Erd(o|¨)s-Ko-Rado (EKR) Theorem Erd(o|¨)-Ko-Rado(EKR)定理4) series of Erds-Turn's type Erd s-Turán型级数5) S→O→R model S→O→R模型1.Based on the S→O→R model,a three-level group effect prevention system of human-caused accidents is established so as to ...
Kamat, V., Misra, N.: An Erdo˝s-Ko-Rado theorem for matchings in the complete graph. In: The Seventh European Conference on Combinatorics, Graph Theory and Applications of CRM Series 16, 613 (2013)V. Kamat and N. Misra. An Erdo˝s-Ko-Rado theorem for matchings in the complete...