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(概率方法和代数方法)来证明Erdos-Ko-Rado定理....
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...
ofErd6s—Ko-RadoTheorem.TheseconddevotestotheNMprop— erty andtheLYM property of intersecting antichains。Inamore generalsetting wegive a unifiedtreatmentoftheSperner-typepropertiesandtheintersectingpropertyinaranked poset。Then,the LYM property and
( ,0)in the sym plectic spaces by investigating of montonoicity of an upper bound function. Key words:finite field;symplectic space;r-intersecting;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...
Erdos-Ko-Rado theorem for {0, ±1}-vectors 喜欢 0 阅读量: 48 作者:P Frankl,A Kupavskii 摘要: The 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 ...
Erdos-Ko-Rado theorem; intersecting family; affine space; 机译:Erdos-Ko-rado定理;相交的家庭;仿射空间; 相似文献 外文文献 中文文献 专利 1.The Erdos-Ko-Rado theorem for finite affine spaces and spring 机译:用于有限染色条件的Erdos-Ko-rado定理 Guo Jun ,Xu Qiuli - Linear & Multilinear Al...
The celebrated Erdos-Ko-Rado theorem states that given n≥2k,every intersecting k-uni-n-1 form hypergraph G on n vertices has at most(n-1 k-1)edges.This pa... Peng,L Zhang,Xiao,... - 应用数学与计算数学学报(英文) 被引量: 0发表: 2021年 On the random version of the Era's match...
Erdos-Ko-Rado theoremResidue class ringGrassrnann graphGrassmannian codep(s)-Kneser graphLet Z(p), be the residue class ring of integers modulo p(s), where p is a prime number ands is a positive integer. We study subspaces and Grassmann graphs for Z(ps)(n). A Grassmann graph for Z...
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...