A discrete isodiametric result: the Erd\H{o}s-Ko-Rado theorem for multisets

TL;DR

This paper extends the Erdős-Ko-Rado theorem to multisets, establishing new bounds for t-intersecting families and connecting these results to coding theory and geometry.

Contribution

It proves a new conjecture on the maximum size of t-intersecting multiset families for large n, generalizing classical combinatorial results.

Findings

Proved the conjecture for n ≥ t(k−t)+2.

Established bounds on multiset family sizes.

Connected combinatorial results to coding theory and geometry.

Abstract

There are many generalizations of the Erd\H{o}s-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 $n \geq t(k-t)+2$ such a family can have at most ${n+k-t-1\choose k-t}$ members.