We prove that every 2-transitive group has a property called the EKR-module property. This gives characterization of maximum intersecting sets permutations in group. Specifically, characteristic vector any set is linear combination vectors stabilizers points and their cosets. also consider when derangement graph connected subgroup or coset subgroup.

Knowledge sharing, which is critical for the strategic utilization of knowledge resources for the benefit of the organization, can only take place when both knowledge contribution and knowledge seeking exist. However, most previous research has focused on only one side of this process – knowledge contribution motivations. This is despite the fact that various barriers to knowledge seeking and r...

Let 1 ≤ t ≤ 7 be an integer and let F be a k-uniform hypergraph on n vertices. Suppose that |A∩B∩C∩D| ≥ t holds for all A,B,C,D ∈ F . Then we have |F | ≤ (n−t k−t ) if | k n − 2 |< ε holds for some ε > 0 and all n > n0(ε). We apply this result to get EKR type inequalities for “intersecting and union families” and “intersecting Sperner families.”

For a family F of sets, let ex(F) := {A : A is an extremal intersecting sub-family of F}. The Erd®s-Ko-Rado (EKR) Theorem states that {A ∈ ( [n] r ) : 1 ∈ A} ∈ ex( ( [n] r ) ) if r ≤ n/2. The Hilton-Milner (HM) Theorem states that if r ≤ n/2 and A is a nontrivial intersecting sub-family of ( [n] r ) then |A| ≤ |{A ∈ ( [n] r ) : 1 ∈ A,A ∩ [2, r + 1] 6= ∅} ∪ {[2, r + 1]}|; hence {{A ∈ ( [n] r ) :...

Knowledge Management Systems (KMS) such as electronic knowledge repositories (EKR) have brought substantial changes to the way organizations leverage their knowledge resources. Despite the importance of KMS, organizations are faced with a challenge to realize the benefits of KMS. One challenging issue that has not been extensively investigated by prior KMS studies is the factors that drive empl...

A family A of r-subsets of the vertex set V (G) of a graph G is intersecting if any two of the r-subsets have a non-empty intersection. The graph G is r-EKR if a largest intersecting family A of independent r-subsets of V (G) may be obtained by taking all independent r-subsets containing some particular vertex. In this paper, we show that if G consists of one path P raised to the power k0 ≥ 1, ...

One of the more recent generalizations of the Erdös-Ko-Rado theorem, formulated by Holroyd, Spencer and Talbot [10], de nes the Erdös-Ko-Rado property for graphs in the following manner: for a graph G, vertex v ∈ G and some integer r ≥ 1, denote the family of independent r-sets of V (G) by J (r)(G) and the subfamily {A ∈ J (r)(G) : v ∈ A} by J (r) v (G), called a star. Then, G is said to be r-E...