Christian Bey, Konrad Engel
An asymptotic complete intersection theorem for chain products

The paper is published: European Journal of Combinatorics, May 1998

05D05 Extremal set theory
06A07 Combinatorics of partially ordered sets
Abstract: Let $N_l(n,k)$ be the set of all $n$--tuples over the alphabet \{0,1,\ldots,k\} whose
component sum equals $l$. A subset $\mathcal{F}\subseteq N_l(n,k)$ is called a
$t$--intersecting family if every two tuples in $\mathcal{F}$ have nonzero
entries in at least $t$ common coordinates. We determine the maximum size of a
$t$--intersecting family in $N_{\lfloor \lambda n\rfloor}(n,k)$ asymptotically for
all fixed $\lambda$ ($0<\lambda

Keywords: intersection theorem, intersecting families, chain product, integer sequence