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On uniqueness of maximal antichains of subsets of a multiset

✍ Scribed by G. F. Clements

Publisher
Springer Netherlands
Year
1984
Tongue
English
Weight
276 KB
Volume
15
Category
Article
ISSN
0031-5303

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πŸ“œ SIMILAR VOLUMES

Antichains in the set of subsets of a mu
Antichains in the set of subsets of a multiset
✍ G.F Clements πŸ“‚ Article πŸ“… 1984 πŸ› Elsevier Science 🌐 English βš– 946 KB

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...=xΒ’ hold. The weight of F, wF, is the total number of elements of M in the various elements x of F. For given inte

An extremal problem for antichains of su
An extremal problem for antichains of subsets of a multiset
✍ G.F. Clements πŸ“‚ Article πŸ“… 1987 πŸ› Elsevier Science 🌐 English βš– 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

A splitting property of maximal antichai
A splitting property of maximal antichains
✍ Rudolf Ahlswede; PΓ©ter L. ErdΕ‘s; Niall Graham πŸ“‚ Article πŸ“… 1995 πŸ› Springer-Verlag 🌐 English βš– 290 KB
Maximum Antichains in Random Subsets of
Maximum Antichains in Random Subsets of a Finite Set
✍ Deryk Osthus πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 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