AbstractA family F is intersecting if F∩F′≠∅ whenever F,F′∈F. Erdős, Ko, and Rado (1961) [6] showed that(1)|F|⩽(n−1k−1) holds for an intersecting family of k-subsets of [n]:={1,2,3,…,n}, n⩾2k. For n>2k the only extremal family consists of all k-subsets containing a fixed element. Here a new proof is presented by using the Katonaʼs shadow theorem for t-intersecting families
In this dissertation, we examine various problems in extremal set theory, which typically entails ma...
AbstractIntersection problems occupy an important place in the theory of finite sets. One of the cen...
AbstractLet X = [1, n] be a finite set of cardinality n and let F be a family of k-subsets of X. Sup...
Theorem 1 (EKR,Frankl,Wilson). Given 1 t k, and suppose n (k t+ 1)(t+ 1), then the maximal size ...
AbstractA family F of distinct k-element subsets of the n-element set X is called intersecting if F ...
A family ℱ of sets is said to be (strictly] EKR if no non-trivial intersecting sub-family of ℱ is (a...
AbstractThe exact bound in the Erdős-Ko-Rado theorem is known [F, W]. It states that if n ⩾ (t + 1)(...
AbstractA family F is intersecting if F∩F′≠∅ whenever F,F′∈F. Erdős, Ko, and Rado (1961) [6] showed ...
AbstractThe Erdös-Ko-Rado theorem states that if F is a family of k-subsets of an n-set no two of wh...
AbstractLet A and B be families of k and l element subsets of an n element set, respectively. Suppos...
AbstractThe Erdős–Ko–Rado theorem tells us how large an intersecting family of r-sets from an n-set ...
Let $n > k > 1$ be integers, $[n] = \{1, \ldots, n\}$. Let $\mathcal F$ be a family of $k$-subsets o...
For positive integers k and n define E (k, n) = {a = (a1 , . . . , an): ai ∈ {0,1, . . . , k - 1 }, ...
In this dissertation, we examine various problems in extremal set theory, which typically entails ma...
A k-uniform family of subsets of [n] is intersecting if it does not contain a disjoint pair of sets....
In this dissertation, we examine various problems in extremal set theory, which typically entails ma...
AbstractIntersection problems occupy an important place in the theory of finite sets. One of the cen...
AbstractLet X = [1, n] be a finite set of cardinality n and let F be a family of k-subsets of X. Sup...
Theorem 1 (EKR,Frankl,Wilson). Given 1 t k, and suppose n (k t+ 1)(t+ 1), then the maximal size ...
AbstractA family F of distinct k-element subsets of the n-element set X is called intersecting if F ...
A family ℱ of sets is said to be (strictly] EKR if no non-trivial intersecting sub-family of ℱ is (a...
AbstractThe exact bound in the Erdős-Ko-Rado theorem is known [F, W]. It states that if n ⩾ (t + 1)(...
AbstractA family F is intersecting if F∩F′≠∅ whenever F,F′∈F. Erdős, Ko, and Rado (1961) [6] showed ...
AbstractThe Erdös-Ko-Rado theorem states that if F is a family of k-subsets of an n-set no two of wh...
AbstractLet A and B be families of k and l element subsets of an n element set, respectively. Suppos...
AbstractThe Erdős–Ko–Rado theorem tells us how large an intersecting family of r-sets from an n-set ...
Let $n > k > 1$ be integers, $[n] = \{1, \ldots, n\}$. Let $\mathcal F$ be a family of $k$-subsets o...
For positive integers k and n define E (k, n) = {a = (a1 , . . . , an): ai ∈ {0,1, . . . , k - 1 }, ...
In this dissertation, we examine various problems in extremal set theory, which typically entails ma...
A k-uniform family of subsets of [n] is intersecting if it does not contain a disjoint pair of sets....
In this dissertation, we examine various problems in extremal set theory, which typically entails ma...
AbstractIntersection problems occupy an important place in the theory of finite sets. One of the cen...
AbstractLet X = [1, n] be a finite set of cardinality n and let F be a family of k-subsets of X. Sup...
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