AbstractConsider the poset Pn of partitions of an n-element set ordered by refinement. Let S(n, k) be the number of partitions containing k blocks. Let Ln be the maximum length of an antichain in Pn Rota conjectured that Ln = maxk S(n, k). In this paper we construct larger antichains for all n sufficiently large
Let n ⩾4 be a natural number, and let K be a set K⊆[n]:={1,2,...,n}. We study the problem of finding...
In this thesis, we present a number of results, mostly concerning set systems that are antichains an...
Given a sequence , a block B of S is a subsequence . The size b of a block B is the sum of its eleme...
AbstractConsider the poset Pn of partitions of an n-element set ordered by refinement. Let S(n, k) b...
AbstractConsider the posetΠnof partitions of ann-element set, ordered by refinement. The sizes of th...
AbstractLet Pin be the poset of partitions of an integer n, ordered by refinement. Let b(Pin) be the...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
AbstractA short proof of the following result of Kleitman is given: the total number of sets contain...
For given positive integers $k$ and $n$, a family $\mathcal{F}$ of subsets of $\{1,\dots,n\}$ is $k$...
AbstractA set X of subsets of an n-element set S is called an anti-chain if no two elements of X are...
AbstractLet 2n_ be the ordered set obtained from the Boolean lattice 2n by deleting both the greates...
AbstractConsider the posetΠnof partitions of ann-element set, ordered by refinement. The sizes of th...
Let n> 4 be a natural number, and let K be a set K ⊆ [n]: = {1, 2,..., n}. We study the problem t...
summary:The reaping number $\frak r_{m,n}({\Bbb B})$ of a Boolean algebra ${\Bbb B}$ is defined as t...
summary:The reaping number $\frak r_{m,n}({\Bbb B})$ of a Boolean algebra ${\Bbb B}$ is defined as t...
Let n ⩾4 be a natural number, and let K be a set K⊆[n]:={1,2,...,n}. We study the problem of finding...
In this thesis, we present a number of results, mostly concerning set systems that are antichains an...
Given a sequence , a block B of S is a subsequence . The size b of a block B is the sum of its eleme...
AbstractConsider the poset Pn of partitions of an n-element set ordered by refinement. Let S(n, k) b...
AbstractConsider the posetΠnof partitions of ann-element set, ordered by refinement. The sizes of th...
AbstractLet Pin be the poset of partitions of an integer n, ordered by refinement. Let b(Pin) be the...
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
AbstractA short proof of the following result of Kleitman is given: the total number of sets contain...
For given positive integers $k$ and $n$, a family $\mathcal{F}$ of subsets of $\{1,\dots,n\}$ is $k$...
AbstractA set X of subsets of an n-element set S is called an anti-chain if no two elements of X are...
AbstractLet 2n_ be the ordered set obtained from the Boolean lattice 2n by deleting both the greates...
AbstractConsider the posetΠnof partitions of ann-element set, ordered by refinement. The sizes of th...
Let n> 4 be a natural number, and let K be a set K ⊆ [n]: = {1, 2,..., n}. We study the problem t...
summary:The reaping number $\frak r_{m,n}({\Bbb B})$ of a Boolean algebra ${\Bbb B}$ is defined as t...
summary:The reaping number $\frak r_{m,n}({\Bbb B})$ of a Boolean algebra ${\Bbb B}$ is defined as t...
Let n ⩾4 be a natural number, and let K be a set K⊆[n]:={1,2,...,n}. We study the problem of finding...
In this thesis, we present a number of results, mostly concerning set systems that are antichains an...
Given a sequence , a block B of S is a subsequence . The size b of a block B is the sum of its eleme...
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