A discrete isodiametric result: the Erdős-Ko-Rado theorem for multisets

Abstract

There are many generalizations of the Erdős-Ko-Rado theorem. We give new results (and problems) concerning families of $t$-intersecting $k$-element multisets of an $n$-set and point out connections to coding theory and classical geometry. We establish the conjecture that for $n\ge t(k-t)+2$ such a family can have at most $\left(\genfrac{}{}{0ex}{}{n+k-t-1}{k-t}\right)$ members.