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
Cardinalities of infinite antichains in products of chains
β Scribed by J.D. Farley
- Book ID
- 105754782
- Publisher
- Springer
- Year
- 1999
- Tongue
- English
- Weight
- 35 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0002-5240
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
Robertson and Seymour have shown that there is no infinite set of graphs in which no member is a minor of another. By contrast, it is well known that the class of all matroids does contains such infinite antichains. However, for many classes of matroids, even the class of binary matroids, it is not