✦ LIBER ✦

Antichains in the set of subsets of a multiset

✍ Scribed by G.F Clements

Publisher: Elsevier Science
Year: 1984
Tongue: English
Weight: 946 KB
Volume: 48
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90128-6

No coin nor oath required. For personal study only.

✦ Synopsis

A set F of distinct subsets x of a finite muhiset M (that is, a set with several different kinds of elements) is a c-antichain if for no c+l elements Xo, xl ..... x c of F does XoCXlc...=x¢ hold. The weight of F, wF, is the total number of elements of M in the various elements x of F. For given integers f and c, we find min wF, where the minimum is taken over all f-element c-antichains F. Daykin [9, has solved this problem for ordinary sets and Clements [3] has solved it for multisets, but only for c = 1.

📜 SIMILAR VOLUMES

Antichains in the set of subsets of a mu

Antichains in the set of subsets of a multiset

✍ G.F. Clements 📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 74 KB

An extremal problem for antichains of su

An extremal problem for antichains of subsets of a multiset

✍ G.F. Clements 📂 Article 📅 1987 🏛 Elsevier Science 🌐 English ⚖ 850 KB

A multiset M is a finite set consisting of several different kinds of elements, and an antichain F is a set of incomparable subsets of M. With P and \_F denoting respectively the set of subsets which contain an element of F or are contained in an element of F, we find the best upper bound for min(lF

Maximum Antichains in Random Subsets of

Maximum Antichains in Random Subsets of a Finite Set

✍ Deryk Osthus 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 125 KB

We consider the random poset P(n, p) which is generated by first selecting each subset of [n]=[1, ..., n] with probability p and then ordering the selected subsets by inclusion. We give asymptotic estimates of the size of the maximum antichain for arbitrary p= p(n). In particular, we prove that if p

A Family of Inequalities for Intersectin

A Family of Inequalities for Intersecting Antichain of Subsets of an n-set

✍ Changyu Wang; Huishan Zhou 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 252 KB

The lattice of antichain cutsets of a pa

The lattice of antichain cutsets of a partially ordered set

✍ Gerhard Behrendt 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 125 KB

## Behrendt, G., The lattice of antichain cutsets of a partially ordered set, Discrete Mathematics 89 (1991) 201-202. Every finite lattice is isomorphic to the lattice of antichain cutsets of a finite partially ordered set whose chains have at most three elements. A subset A of a partially order

Extremal problems among subsets of a set

✍ Paul Erdos; Daniel J. Kleitman 📂 Article 📅 1974 🏛 Elsevier Science 🌐 English ⚖ 945 KB