Add to ORKGIf P is a partially ordered set, a k-family of P is a subset which contains no chains of length k + 1. This paper examines the structure of the set of k-families of P. An extension of Dilworth\u27s theorem is obtained by relating the maximum size of a k-family to certain partitions of P into chains. A natural lattice ordering on k-families is defined and analyzed, and a number of strong intersection properties are obtained. Finally, thek-families of P are used to define a class of submodular set functions on P, which can be used to generalize a number of results in transversal theory
A family of sets F ⊆ 2X is defined to be l-trace k-Sperner if for any subset Y of X with size l the ...
We seek families of subsets of an n-set of given size that contain the fewest k-chains. We prove a “...
An equivalence on the family of subsets of an e-element set E is hereditary if |a| = |b| and |x{⊆a:x...
AbstractIf P is a partially ordered set, a k-family of P is a subset which contains no chains of len...
AbstractLet P be a poset. A subset A of P is a k-family iff A contains no (k + 1)-element chain. For...
AbstractA ranked poset P has the Sperner property if the sizes of the largest rank and of the larges...
A central result in extremal set theory is the celebrated theorem of Sperner from 1928, which gives ...
A central result in extremal set theory is the celebrated theorem of Sperner from 1928, which gives ...
AbstractLet P be a poset. A subset A of P is a k-family iff A contains no (k + 1)-element chain. For...
As part of his seminal work, Sperner introduced Sperner set systems, which are a family of sets that...
AbstractWe explore a problem of Frankl (1989). A family F of subsets of 0–1, 2, …, m is said to have...
AbstractLet nc,d(r, k) denote the maximal cardinality of Sperner families F (i.e., X⫅̸Y for all X, Y...
We prove a “supersaturation-type ” extension of both Sperner’s Theorem (1928) and its gen-eralizatio...
AbstractA family of sets F⊆2X is defined to be l-trace k-Sperner if for any subset Y of X with size ...
AbstractLet |X| = n > 0, |Y| = k > 0, and Y ⊆ X. A family A of subsets of X is a Sperner family of X...
A family of sets F ⊆ 2X is defined to be l-trace k-Sperner if for any subset Y of X with size l the ...
We seek families of subsets of an n-set of given size that contain the fewest k-chains. We prove a “...
An equivalence on the family of subsets of an e-element set E is hereditary if |a| = |b| and |x{⊆a:x...
AbstractIf P is a partially ordered set, a k-family of P is a subset which contains no chains of len...
AbstractLet P be a poset. A subset A of P is a k-family iff A contains no (k + 1)-element chain. For...
AbstractA ranked poset P has the Sperner property if the sizes of the largest rank and of the larges...
A central result in extremal set theory is the celebrated theorem of Sperner from 1928, which gives ...
A central result in extremal set theory is the celebrated theorem of Sperner from 1928, which gives ...
AbstractLet P be a poset. A subset A of P is a k-family iff A contains no (k + 1)-element chain. For...
As part of his seminal work, Sperner introduced Sperner set systems, which are a family of sets that...
AbstractWe explore a problem of Frankl (1989). A family F of subsets of 0–1, 2, …, m is said to have...
AbstractLet nc,d(r, k) denote the maximal cardinality of Sperner families F (i.e., X⫅̸Y for all X, Y...
We prove a “supersaturation-type ” extension of both Sperner’s Theorem (1928) and its gen-eralizatio...
AbstractA family of sets F⊆2X is defined to be l-trace k-Sperner if for any subset Y of X with size ...
AbstractLet |X| = n > 0, |Y| = k > 0, and Y ⊆ X. A family A of subsets of X is a Sperner family of X...
A family of sets F ⊆ 2X is defined to be l-trace k-Sperner if for any subset Y of X with size l the ...
We seek families of subsets of an n-set of given size that contain the fewest k-chains. We prove a “...
An equivalence on the family of subsets of an e-element set E is hereditary if |a| = |b| and |x{⊆a:x...