Ahlswede R, Erdős PL, Graham N. A splitting property of maximal antichains. Combinatorica. 1995;15(4):475-480.In any dense poset P (and in any Boolean lattice in particular) every maximal antichain S may be partitioned into disjoint subsets S-1 and S-2, such that the union of the downset of S-1 with the upset of S-2 yields the entire poset: D(S-1)boolean OR U(S-2)=P. To find a similar splitting of maximal antichains in posets is NP-hard in general
AbstractFor each integer k≥3, we find all maximal intervals Ik of natural numbers with the following...
We present two results on maximal antichains in the strict chain product poset $[t_1+1]\times[t_2+1]...
We exhibit a recursive procedure that enables us to construct a maximal union of k chains in a finit...
It is known that in every finite poset P any maximal antichain S with some denseness property may be...
AbstractIt is known that in every finite poset P any maximal antichain S with some denseness propert...
A structural condition is given for finite maximal antichains in the homomorphism order of relationa...
AbstractFix integers n and k with n≥k≥3. Duffus and Sands proved that if P is a finite poset and n≤|...
AbstractLet f(n) be the smallest integer t such that a poset obtained from a Boolean lattice with n ...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.Includes bibliogr...
We consider ‘supersaturation’ problems in partially ordered sets (posets) of the following form. Giv...
AbstractAfibre in a partially ordered set P is a subset of P meeting every maximal antichain of P. W...
AbstractLet 2n_ be the ordered set obtained from the Boolean lattice 2n by deleting both the greates...
AbstractThe following general theorem is proven: Given a partially ordered set and a group of permut...
We consider ‘supersaturation’ problems in partially ordered sets (posets) of the following form. Giv...
AbstractRecently there has been a good deal of interest in the maximal sized antichains of a partial...
AbstractFor each integer k≥3, we find all maximal intervals Ik of natural numbers with the following...
We present two results on maximal antichains in the strict chain product poset $[t_1+1]\times[t_2+1]...
We exhibit a recursive procedure that enables us to construct a maximal union of k chains in a finit...
It is known that in every finite poset P any maximal antichain S with some denseness property may be...
AbstractIt is known that in every finite poset P any maximal antichain S with some denseness propert...
A structural condition is given for finite maximal antichains in the homomorphism order of relationa...
AbstractFix integers n and k with n≥k≥3. Duffus and Sands proved that if P is a finite poset and n≤|...
AbstractLet f(n) be the smallest integer t such that a poset obtained from a Boolean lattice with n ...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.Includes bibliogr...
We consider ‘supersaturation’ problems in partially ordered sets (posets) of the following form. Giv...
AbstractAfibre in a partially ordered set P is a subset of P meeting every maximal antichain of P. W...
AbstractLet 2n_ be the ordered set obtained from the Boolean lattice 2n by deleting both the greates...
AbstractThe following general theorem is proven: Given a partially ordered set and a group of permut...
We consider ‘supersaturation’ problems in partially ordered sets (posets) of the following form. Giv...
AbstractRecently there has been a good deal of interest in the maximal sized antichains of a partial...
AbstractFor each integer k≥3, we find all maximal intervals Ik of natural numbers with the following...
We present two results on maximal antichains in the strict chain product poset $[t_1+1]\times[t_2+1]...
We exhibit a recursive procedure that enables us to construct a maximal union of k chains in a finit...
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