منابع مشابه
Cutsets of Boolean lattices
In graph theory, Menger’s Theorem is the basis of many results concerning notions of connectedness. There are many versions, in this paper the following will be useful. Let G = (V, E) be a directed graph and A, B disjoint subsets of V with no directed edge from A to B. A subset of V -A U B is called an (A, B) separating vertex-set if every directed path from A to B intersects F. A set of direct...
متن کاملGames of Chains and Cutsets in the Boolean Lattice II
B. Bájnok and S. Shahriari proved that in 2, the Boolean lattice of order n, the width (the maximum size of an antichain) of a non-trivial cutset (a collection of subsets that meets every maximal chain and does not contain ∅ or [n]) is at least n− 1. We prove that, for n ≥ 5, in the Boolean lattice of order n, given ⌈n2 ⌉− 1 disjoint long chains, we can enlarge the collection to a cutset of wid...
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A study is made of Boolean product representations of bounded lattices over the Stone space of their centres. Special emphasis is placed on relating topological properties such as clopen or regular open equalizers to their equivalent lattice theoretic counterparts. Results are also presented connecting various properties of a lattice with properties of its individual stalks. Mathematics Subject...
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A cutset in the poset 2, of subsets of {1, . . . , n} ordered by inclusion, is a subset of 2 that intersects every maximal chain. Let 0 ≤ α ≤ 1 be a real number. Is it possible to find a cutset in 2 that, for each 0 ≤ i ≤ n, contains at most α ( n i ) subsets of size i? Let α(n) be the greatest lower bound of all real numbers for which the answer is positive. In this note we prove the rather su...
متن کاملBoolean filters of distributive lattices
In this paper we introduce the notion of Boolean filters in a pseudo-complemented distributive lattice and characterize the class of all Boolean filters. Further a set of equivalent conditions are derived for a proper filter to become a prime Boolean filter. Also a set of equivalent conditions is derived for a pseudo-complemented distributive lattice to become a Boolean algebra. Finally, a Bool...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1987
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90011-2