The maximal length of cloud-antichains
β Scribed by Rudolf Ahlswede; Levon H. Khachatrian
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 365 KB
- Volume
- 131
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
For six natural notions of cloud-antichains in a partially ordered set .Y we determine asymptotically their maximal lengths if 9 is the family of all subsets of a finite set. Actually, in three cases we even have exact results.
π SIMILAR VOLUMES
Recently there has been a good deal of interest m the maximal sized antichains of a partially ordered set [ 1-8] A theorem of Dtlworth states that under the natural ordering these antlchams form a distributive lattice. This paper outhnes a proof of this theorem and apphes it to strengthen the result
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