For given positive integers $ k $ and $ n $, a family $\mathcal {F} $ of subsets of $\{1,\dots,
n\} $ is $ k $-antichain saturated if it does not contain an antichain of size $ k $, but adding …

A subset F of an ordered set X is a fibre of X if F intersects every maximal antichain of X. We
find a lower bound on the function ƒ (D), the minimum fibre size in the distributive lattice D, in …

For integers $0\leq m\leq l\leq nm $, the truncated Boolean lattice ${\cal B} _n (m, l) $ is the
poset of all subsets of $[n]=\{1, 2,\ldots, n\} $ which have size at least $ m $ and at most $ l …

and let be the collection of all subsets of [n] ordered by inclusion. is a cutset if it meets every
maximal chain in, and the width of is the minimum number of chains in a chain …

Anderson and Griggs proved independently that a rank-symmetric-unimodal normalized
matching (NM) poset possesses a nested chain decomposition (or nesting), and Griggs later …

For each integer k≥ 3, we find all maximal intervals Ik of natural numbers with the following
property: whenever the number of elements in every maximal chain in a finite partially …

Abstract B. Bajnok and S. Shahriari proved that in 2 n, the Boolean lattice of order n, the
width (the maximum size of an antichain) of a non-trivial cutset (a collection of subsets that …

A cutset in the poset 2 [n], of subsets of {1,..., n} ordered by inclusion, is a subset of 2 [n] that
intersects every maximal chain. Let 0≤ α≤ 1 be a real number. Is it possible to find a cutset …

Let 2 [n] denote the poset of all subsets of [n]={1, 2,..., n} ordered by inclusion. Following
Gutterman and Shahriari (Order 14, 1998, 321–325) we consider a game G n (a, b, c). This …

In this paper we will survey a collection of recent results about chains and cutsets in the
Boolean lattice and some other posets. In particular, we consider the possibilities for the …