Variants of Baranyai's Theorem with Additional Conditions

Zoe Xi

A classical theorem of Baranyai states that, given integers $2\le k<n$ such that $k$ divides $n$, one can find a family of $\left(\genfrac{}{}{0ex}{}{n-1}{k-1}\right)$ partitions of $[n]$ into $k$-elemen…