ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

13. Combinatorics

1991 MS Classification: 5 Bey, Christian, Universität Rostock, Germany An intersection theorem for the Function lattice. The Function lattice F_{α}^{n} consists of all n-tuples over the alphabet {0, 1, …, α} endowed with an order relation defined by (x_{1}, …, x_{n}) ≤ (y_{1}, …, y_{n}) iff x_{i} = 0 or x_{i} = y_{i} for all i = 1, …, n. The rank of an element x of F_{α}^{n} is given by the number of nonzero entries in x. A subset F of F_{α}^{n} is called k-uniform t-intersecting if all elements of F have rank k and the infimum of every two elements of F has rank at least t. We determine for all real λ (0 < λ < 1) and sufficiently large n the maximum size of a ⌊λn⌋-uniform t-intersecting subset of F_{α}^{n}.