Add to ORKGAbstract Let F be a family of subsets of an n-element set. F is called (p,q)-chain intersecting if it does not contain chains A1 ( A2 ( · · · ( Ap and B1 ( B2 ( · · · ( Bq with Ap∩Bq = ∅. The maximum size of these families is determined in this paper. Similarly to the p = q = 1 special case (intersecting families) this depends on the notion of r-complementing-chain-pair-free families, where r = p + q − 1. A family F is called r-complementing-chain-pair-free if there is no chain L ⊆ F of length r such that the complement of every set in L also belongs to F. The maximum size of such families is also determined here and optimal constructions are characterized. Key words. Extremal family, Disjoint chains 1. Introduction an
For a family $\mathcal F$, let $\mathcal D(\mathcal F)$ stand for the family of all sets that can be...
Let $n > k > 1$ be integers, $[n] = \{1, \ldots, n\}$. Let $\mathcal F$ be a family of $k$-subsets o...
A family A of sets is said to be t-intersecting if any two sets in A contain at least t common eleme...
We study the maximum cardinality of a pairwise-intersecting family of subsets of an n-set, or the si...
A set system \({\mathcal F}\) is \(t\)-intersecting, if the size of the intersection of every pair o...
AbstractWe study maximum cardinality families of pairwise intersecting subsets of an n-set. We give ...
In extremal set theory our usual goal is to find the maximal size of a family of subsets of an $n$-e...
AbstractIntersection problems occupy an important place in the theory of finite sets. One of the cen...
AbstractLet n⩾t⩾1 be integers. Let F, G be families of subsets of the n-element set X. They are call...
In this dissertation, we examine various problems in extremal set theory, which typically entails ma...
AbstractA large variety of problems and results in Extremal Set Theory deal with estimates on the si...
AbstractLet X = [1, n] be a finite set of cardinality n and let F be a family of k-subsets of X. Sup...
AbstractWe consider the maximal size of families of k-element subsets of an n element set [n] that s...
AbstractLet [n] denote the set {1,2,…,n}, 2[n] the collection of all subsets of [n] and F⊂2[n] be a ...
Let us write DF (G) = {F ∈ F: F ∩ G = ∅} for a set G and a family F. Then a family F of sets is sai...
For a family $\mathcal F$, let $\mathcal D(\mathcal F)$ stand for the family of all sets that can be...
Let $n > k > 1$ be integers, $[n] = \{1, \ldots, n\}$. Let $\mathcal F$ be a family of $k$-subsets o...
A family A of sets is said to be t-intersecting if any two sets in A contain at least t common eleme...
We study the maximum cardinality of a pairwise-intersecting family of subsets of an n-set, or the si...
A set system \({\mathcal F}\) is \(t\)-intersecting, if the size of the intersection of every pair o...
AbstractWe study maximum cardinality families of pairwise intersecting subsets of an n-set. We give ...
In extremal set theory our usual goal is to find the maximal size of a family of subsets of an $n$-e...
AbstractIntersection problems occupy an important place in the theory of finite sets. One of the cen...
AbstractLet n⩾t⩾1 be integers. Let F, G be families of subsets of the n-element set X. They are call...
In this dissertation, we examine various problems in extremal set theory, which typically entails ma...
AbstractA large variety of problems and results in Extremal Set Theory deal with estimates on the si...
AbstractLet X = [1, n] be a finite set of cardinality n and let F be a family of k-subsets of X. Sup...
AbstractWe consider the maximal size of families of k-element subsets of an n element set [n] that s...
AbstractLet [n] denote the set {1,2,…,n}, 2[n] the collection of all subsets of [n] and F⊂2[n] be a ...
Let us write DF (G) = {F ∈ F: F ∩ G = ∅} for a set G and a family F. Then a family F of sets is sai...
For a family $\mathcal F$, let $\mathcal D(\mathcal F)$ stand for the family of all sets that can be...
Let $n > k > 1$ be integers, $[n] = \{1, \ldots, n\}$. Let $\mathcal F$ be a family of $k$-subsets o...
A family A of sets is said to be t-intersecting if any two sets in A contain at least t common eleme...