๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Maximum antichains in the product of chains

โœ Scribed by Jerrold R. Griggs

Publisher
Springer Netherlands
Year
1984
Tongue
English
Weight
433 KB
Volume
1
Category
Article
ISSN
0167-8094

No coin nor oath required. For personal study only.

โœฆ Synopsis

Let P be the poset k, x ~~~xk,,whichisaproductofchains,wheren>landk, >+a.> kn > 2. Let M = k, -8yT=z(kt -1). P is known to have the Sperner property, which means that its maximum ranks are maximum antichains. Here we prove that its maximum ranks are its only maximum antichains if and only if either n = 1 or M < 1. This is a generalization of a classical result, Sperner's Theorem, which is the case k, = ... = kn = 2. We also determine the number and location of.the maximum ranks of P. AMS (MOS) subject classifications (1980). 06A10,05A05.

๐Ÿ“œ SIMILAR VOLUMES

Products of chains with monochromatic ma
Products of chains with monochromatic maximal chains and antichains
โœ D. Duffus; T. Goddard ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Springer Netherlands ๐ŸŒ English โš– 996 KB

There is a product of two linear orders of size 2nn with the property that every subset or complement thereof contains a maximal chain. Furthermore, for regular l&, there is a product of two linear orders of size t&+2 that when colored with fewer than & colors always has a monochromatic maximal chai

Maximum Antichains in Random Subsets of
Maximum Antichains in Random Subsets of a Finite Set
โœ Deryk Osthus ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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

The conformations of alkyl chains in flu
The conformations of alkyl chains in fluids. A maximum entropy approach
โœ R. Berardi; F. Spinozzi; C. Zannoni ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 422 KB

We present a maximum entropy internal order method for analyzing chain conformations in liquid crystalline solutions. We show how prior knowledge of the conformational distribution can be taken into account and apply the method to the determination of the conformation of n-alkanes in liquid crystal