On the minimum width of a cutset in the truncated Boolean lattice

B Bajnok - arXiv preprint arXiv:1512.02978, 2015 - arxiv.org
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 …

[PDF][PDF] On the f-vectors of Cutsets in the Boolean Lattice

M Haines, S Shahriari - Journal of combinatorial theory. Series A, 2001 - academia.edu
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 …

Games of chains and cutsets in the Boolean lattice II

DL Li, S Shahriari - Order, 2001 - Springer
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 …

Width and f-vectors of cutsets in the truncated Boolean lattice

S Shahriari - Electronic Notes in Discrete Mathematics, 2002 - Elsevier
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 …

Edge‐cutsets in the directed hypercube

PL Mariz, S Shahriari - Networks: An International Journal, 2002 - Wiley Online Library
Let n≥ 2 and 0≤ k≤ n− 2 be integers. We show that given any collection of k skipless
chains in 2 [n], the Boolean lattice of order n, there exists n− k edge‐disjoint maximal chains …

Cutsets and anti-chains in linear lattices

B Rothschild, S Shahriari - Journal of Combinatorial Theory, Series A, 2006 - Elsevier
Consider the poset, ordered by inclusion, of subspaces of a four-dimensional vector space
over a field with 2 elements. We prove that, for this poset, any cutset (ie, a collection of …

[引用][C] Coding Theoretic Constructions of Some Number Theoretic Ramanujan Graphs

O Moreno - Congressus Numerantium, 1970 - Utilitas Mathematica Pub …