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-RadoHilton-MilnerShifting techniqueInjective proofA set system F is intersecting if for any F, F' epsilon F boolean AND F' not equal (sic). A fundamental theorem of Erdos, Ko and Rado states that if F is an intersecting family of r-subsets of [n] = {1, ..., n}, and ...
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...
论文主要研究偏序集的ErdSs-Ko-Rado(EKR)性质,交族的正规匹配(NM)性 质、LYM性质,子空间族的最小下影问题以及Erd6s-Ko-Rado定理在置换群中的模 拟. 本文分四章.第一章介绍EKR定理的内容、发展历史以及几种经典证明方法. 第二章研究分次偏序集中交族的正规匹配(NM)性质和LYM性质.在较广的意义 ...
Symmetric groupsERDOS-KO-RADOTHEOREMFAMILIESPROOFPROPERTYGiven a finite transitive group G <= Sym(12), a subset F of G is intersecting if any two ... A Behajaina,R Maleki,AS Razafimahatratra - 《Linear Algebra & Its Applications》 被引量: 0发表: 2023年 On the Erdos-Ko-Rado property ...
There are various graphs that are known to have this property; the empty graph of order n >= 2r (this is the celebrated Erdos-Ko-Rado theorem), any disjoint union of atleast r copies of K_t for t >= 2, and any cycle. In this paper we show how these results can be extended ...
As the key ingredient of the proof we show that the Lagrangian of intersecting r-graphs is maximized by principally intersecting r-graphs for r >= 4.Watts, Adam BeneNorin, SergeyYepremyan, LianaMIT Dept Phys Cambridge MA 02142 USACombinatorica...