Add to ORKGThis paper proves the sunflower conjecture by confirming that a family ${\mathcal F}$ of sets each of cardinality at most $m$ includes a $k$-sunflower, if $|{\mathcal F}| >[ ck \log (k+1)]^m$ for a constant $c>0$ independent of $m$ and $k$, where $k$-sunflower stands for a family of $k$ different sets with common pair-wise intersections.Comment: 10 pages. The paper is self-contained to verif
AbstractFor a set A let [A]k denote the family of all k-element subsets of A. A function f:[A]k→C is...
AbstractA family ofrsets is called aΔ-system if any two sets have the same intersection. Denote byF(...
A k-signed r-set on[n] = {1, ..., n} is an ordered pair (A, f), where A is an r-subset of [n] and f ...
A sunflower with $r$ petals is a collection of $r$ sets over a ground set $X$ such that every elemen...
Given a family F of k-element sets, S1,…,Sr∈F form an {\em r-sunflower} if Si∩Sj=Si′∩Sj′ for all i≠j...
We prove that given a constant $k \ge 2$ and a large set system $\mathcal{F}$ of sets of size at mos...
We present several variants of the sunflower conjecture of Erdős and Rado and discuss the relations ...
The sunflower conjecture is one of the most well-known open problems in combinatorics. It has severa...
We present several variants of the sunflower conjecture of Erdős & Rado (J Lond Math Soc 35:85–90, 1...
AbstractFollowing a conjecture of P. Erdös, we show that if F is a family of k-subsets of and n-set ...
AbstractIn [Z. Füredi, Turán type problems, in: Surveys in Combinatorics, Guildford, 1991, in: Londo...
AbstractWe give a new proof of a theorem of Mansour and Sun by using number theory and Rothe’s ident...
For given positive integers $k$ and $n$, a family $\mathcal{F}$ of subsets of $\{1,\dots,n\}$ is $k$...
The following conjecture of G. O. H. Katona is proved. Let X be a finite set of cardinality n, and A...
AbstractIn this paper, we first establish a fixed point theorem for a k-set contraction map on the f...
AbstractFor a set A let [A]k denote the family of all k-element subsets of A. A function f:[A]k→C is...
AbstractA family ofrsets is called aΔ-system if any two sets have the same intersection. Denote byF(...
A k-signed r-set on[n] = {1, ..., n} is an ordered pair (A, f), where A is an r-subset of [n] and f ...
A sunflower with $r$ petals is a collection of $r$ sets over a ground set $X$ such that every elemen...
Given a family F of k-element sets, S1,…,Sr∈F form an {\em r-sunflower} if Si∩Sj=Si′∩Sj′ for all i≠j...
We prove that given a constant $k \ge 2$ and a large set system $\mathcal{F}$ of sets of size at mos...
We present several variants of the sunflower conjecture of Erdős and Rado and discuss the relations ...
The sunflower conjecture is one of the most well-known open problems in combinatorics. It has severa...
We present several variants of the sunflower conjecture of Erdős & Rado (J Lond Math Soc 35:85–90, 1...
AbstractFollowing a conjecture of P. Erdös, we show that if F is a family of k-subsets of and n-set ...
AbstractIn [Z. Füredi, Turán type problems, in: Surveys in Combinatorics, Guildford, 1991, in: Londo...
AbstractWe give a new proof of a theorem of Mansour and Sun by using number theory and Rothe’s ident...
For given positive integers $k$ and $n$, a family $\mathcal{F}$ of subsets of $\{1,\dots,n\}$ is $k$...
The following conjecture of G. O. H. Katona is proved. Let X be a finite set of cardinality n, and A...
AbstractIn this paper, we first establish a fixed point theorem for a k-set contraction map on the f...
AbstractFor a set A let [A]k denote the family of all k-element subsets of A. A function f:[A]k→C is...
AbstractA family ofrsets is called aΔ-system if any two sets have the same intersection. Denote byF(...
A k-signed r-set on[n] = {1, ..., n} is an ordered pair (A, f), where A is an r-subset of [n] and f ...