AbstractSuppose that A is a finite set-system on N points, and for everytwo different A, A′ϵ A we have |A∩A′|=0 or r. Then we prove that |A≤⌊Nr⌋2+⌊Nr⌋+(N−r⌊Nr⌋) whenever N>N0(r). The extremal family is unique and consists of 2r, r and 1-elements sets only. The assumption N>N0(r) can not be omitted. We state some further results and problems
AbstractLet n and k be positive integers, k ⩾ 3. Denote by φ(n, k) the least positive integer such t...
We study the maximum cardinality of a pairwise-intersecting family of subsets of an n-set, or the si...
AbstractA family ofrsets is called aΔ-system if any two sets have the same intersection. Denote byF(...
AbstractSuppose that A is a finite set-system on N points, and for everytwo different A, A′ϵ A we ha...
AbstractA large variety of problems and results in Extremal Set Theory deal with estimates on the si...
AbstractLetr⩾3 be an integer. A weak (r,Δ)-system is a family ofrsets such that all pairwise interse...
A family of r sets is called a ∆-system if any two sets have the same intersection. Denote by F (n, ...
AbstractSuppose that A is a finite set-system of N elements with the property |A ∩ A′| = 0, 1 or k f...
AbstractLet X = [1, n] be a finite set of cardinality n and let F be a family of k-subsets of X. Sup...
AbstractIf A1, …, Am; B1, …, Bm are finite sets such that for l ⩾ t ⩾ 0 and any r, s, we have |Ai| ⩽...
AbstractLet n and k be positive integers, k ⩾ 3. Denote by φ(n, k) the least positive integer such t...
AbstractIt was proved by Erdös, Ko, and Radó (Intersection theorems for systems of finite sets, Quar...
Let S be a set with w elements and Fa set of fc-point subsets of S, n ^ k + 1 ^ 5. I f |F |> () \...
AbstractLet X be a finite set of n-melements and suppose t ⩾ 0 is an integer. In 1975, P. Erdös aske...
AbstractWe prove the following result and transfinite extensions of it: Let (Mi:i ϵ I) be a family o...
AbstractLet n and k be positive integers, k ⩾ 3. Denote by φ(n, k) the least positive integer such t...
We study the maximum cardinality of a pairwise-intersecting family of subsets of an n-set, or the si...
AbstractA family ofrsets is called aΔ-system if any two sets have the same intersection. Denote byF(...
AbstractSuppose that A is a finite set-system on N points, and for everytwo different A, A′ϵ A we ha...
AbstractA large variety of problems and results in Extremal Set Theory deal with estimates on the si...
AbstractLetr⩾3 be an integer. A weak (r,Δ)-system is a family ofrsets such that all pairwise interse...
A family of r sets is called a ∆-system if any two sets have the same intersection. Denote by F (n, ...
AbstractSuppose that A is a finite set-system of N elements with the property |A ∩ A′| = 0, 1 or k f...
AbstractLet X = [1, n] be a finite set of cardinality n and let F be a family of k-subsets of X. Sup...
AbstractIf A1, …, Am; B1, …, Bm are finite sets such that for l ⩾ t ⩾ 0 and any r, s, we have |Ai| ⩽...
AbstractLet n and k be positive integers, k ⩾ 3. Denote by φ(n, k) the least positive integer such t...
AbstractIt was proved by Erdös, Ko, and Radó (Intersection theorems for systems of finite sets, Quar...
Let S be a set with w elements and Fa set of fc-point subsets of S, n ^ k + 1 ^ 5. I f |F |> () \...
AbstractLet X be a finite set of n-melements and suppose t ⩾ 0 is an integer. In 1975, P. Erdös aske...
AbstractWe prove the following result and transfinite extensions of it: Let (Mi:i ϵ I) be a family o...
AbstractLet n and k be positive integers, k ⩾ 3. Denote by φ(n, k) the least positive integer such t...
We study the maximum cardinality of a pairwise-intersecting family of subsets of an n-set, or the si...
AbstractA family ofrsets is called aΔ-system if any two sets have the same intersection. Denote byF(...
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