AbstractLet Pin be the poset of partitions of an integer n, ordered by refinement. Let b(Pin) be the largest size of a level and d(Pin) be the largest size of an antichain of Pin. We prove thatd(Pin)b(Pin)⩽e+o(1)asn→∞.The denominator is determined asymptotically. In addition, we show that the incidence matrices in the lower half of Pin have full rank, and we prove a tight upper bound for the ratio from above if Pin is replaced by any graded poset P
AbstractWe prove a lemma that is useful for obtaining upper bounds for the number of partitions with...
We study the problem of determining the size of the largest intersecting P-free family for a given p...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.Includes bibliogr...
AbstractConsider the posetΠnof partitions of ann-element set, ordered by refinement. The sizes of th...
AbstractA poset P=(X,≼) is m-partite if X has a partition X=X1∪⋯∪Xm such that (1) each Xi forms an a...
AbstractConsider the posetΠnof partitions of ann-element set, ordered by refinement. The sizes of th...
Let $f(n)$ be the largest integer such that every poset on n elements has a 2-dimensional subposet o...
A method is given for finding a chain of maximum length between two partitions λ ⩽ μ in the lattice ...
AbstractConsider the poset Pn of partitions of an n-element set ordered by refinement. Let S(n, k) b...
AbstractLet 2n_ be the ordered set obtained from the Boolean lattice 2n by deleting both the greates...
We consider ‘supersaturation’ problems in partially ordered sets (posets) of the following form. Giv...
AbstractA partition of a finite poset into chains places a natural upper bound on the size of a unio...
AbstractWe prove that for each integer l > 1 there exists a number r = r(l) > 1 such that every fini...
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...
AbstractWe prove a lemma that is useful for obtaining upper bounds for the number of partitions with...
We study the problem of determining the size of the largest intersecting P-free family for a given p...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.Includes bibliogr...
AbstractConsider the posetΠnof partitions of ann-element set, ordered by refinement. The sizes of th...
AbstractA poset P=(X,≼) is m-partite if X has a partition X=X1∪⋯∪Xm such that (1) each Xi forms an a...
AbstractConsider the posetΠnof partitions of ann-element set, ordered by refinement. The sizes of th...
Let $f(n)$ be the largest integer such that every poset on n elements has a 2-dimensional subposet o...
A method is given for finding a chain of maximum length between two partitions λ ⩽ μ in the lattice ...
AbstractConsider the poset Pn of partitions of an n-element set ordered by refinement. Let S(n, k) b...
AbstractLet 2n_ be the ordered set obtained from the Boolean lattice 2n by deleting both the greates...
We consider ‘supersaturation’ problems in partially ordered sets (posets) of the following form. Giv...
AbstractA partition of a finite poset into chains places a natural upper bound on the size of a unio...
AbstractWe prove that for each integer l > 1 there exists a number r = r(l) > 1 such that every fini...
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...
AbstractWe prove a lemma that is useful for obtaining upper bounds for the number of partitions with...
We study the problem of determining the size of the largest intersecting P-free family for a given p...
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.Includes bibliogr...