AbstractLet X = {x1, x2,…} be a finite set and associate to every xi a real number αi. Let f(n) [g (n)] be the least value such that given any family F of subsets of X having maximum degree n [cardinality n], one can find integers αi, i=1,2,… so that αi − αi|<1 and ∑xi ϵ Eai−∑xi ϵ Eαi≤ƒ(n) ∑xi ϵ Eai− ∑xi ϵ Eαi≤g(n) for all E ϵ F. We prove f(n)≤n − 1 and g(n)≤c(n log n)12
AbstractLet X be an n-element set and F ⊂ (kx) such that all the (2 |F|) sets F1 ⌣ F2, F1, F2 ∈ F ar...
AbstractWe improve the lower and upper bounds reported by Herzog and Schönheim for mr(p), the minimu...
AbstractLet Δn and k be positive integers, k≥3. By an (l, n) system is meant a family of l distinct ...
AbstractLet X = {x1, x2,…} be a finite set and associate to every xi a real number αi. Let f(n) [g (...
AbstractLet X be a finite set of n-melements and suppose t ⩾ 0 is an integer. In 1975, P. Erdös aske...
AbstractLet n, t, k be integers, n ⩾ t ⩾ 1, k ⩾ 2. Let x = {1, 2, …, n}. Let F be a family of subset...
AbstractLet n, m and k be positive integers. Let X be a set of cardinality n, and let F be a family ...
AbstractLet S be an n-element set. In this paper, we determine the smallest number f(n) for which th...
AbstractSuppose ε > 0 and k > 1. We show that if n > n0(k, ε) and A ⊆ Zn satisfies |A| > ((1k) + ε)n...
AbstractLet L = {l1, l2, …, lk} be a collection of k positive integers, let A be a family of subsets...
AbstractDenote by m(n,s) the size of a smallest family F; of n-element sets with the property that i...
AbstractSuppose that A is a finite set-system on N points, and for everytwo different A, A′ϵ A we ha...
AbstractLet fk(n) denote the maximum of k-subsets of an n-set satisfying the condition in the title....
AbstractFollowing a conjecture of P. Erdös, we show that if F is a family of k-subsets of and n-set ...
The main object of this thesis is to study the following extremal problem in number theory: Let n an...
AbstractLet X be an n-element set and F ⊂ (kx) such that all the (2 |F|) sets F1 ⌣ F2, F1, F2 ∈ F ar...
AbstractWe improve the lower and upper bounds reported by Herzog and Schönheim for mr(p), the minimu...
AbstractLet Δn and k be positive integers, k≥3. By an (l, n) system is meant a family of l distinct ...
AbstractLet X = {x1, x2,…} be a finite set and associate to every xi a real number αi. Let f(n) [g (...
AbstractLet X be a finite set of n-melements and suppose t ⩾ 0 is an integer. In 1975, P. Erdös aske...
AbstractLet n, t, k be integers, n ⩾ t ⩾ 1, k ⩾ 2. Let x = {1, 2, …, n}. Let F be a family of subset...
AbstractLet n, m and k be positive integers. Let X be a set of cardinality n, and let F be a family ...
AbstractLet S be an n-element set. In this paper, we determine the smallest number f(n) for which th...
AbstractSuppose ε > 0 and k > 1. We show that if n > n0(k, ε) and A ⊆ Zn satisfies |A| > ((1k) + ε)n...
AbstractLet L = {l1, l2, …, lk} be a collection of k positive integers, let A be a family of subsets...
AbstractDenote by m(n,s) the size of a smallest family F; of n-element sets with the property that i...
AbstractSuppose that A is a finite set-system on N points, and for everytwo different A, A′ϵ A we ha...
AbstractLet fk(n) denote the maximum of k-subsets of an n-set satisfying the condition in the title....
AbstractFollowing a conjecture of P. Erdös, we show that if F is a family of k-subsets of and n-set ...
The main object of this thesis is to study the following extremal problem in number theory: Let n an...
AbstractLet X be an n-element set and F ⊂ (kx) such that all the (2 |F|) sets F1 ⌣ F2, F1, F2 ∈ F ar...
AbstractWe improve the lower and upper bounds reported by Herzog and Schönheim for mr(p), the minimu...
AbstractLet Δn and k be positive integers, k≥3. By an (l, n) system is meant a family of l distinct ...
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