3 problems

A partial $6$-factorization is a collection of edge-disjoint $6$-factors, called colors, in a sub-hypergraph of the complete $3$-uniform hypergraph $K_{10}^3$; an extension is a…

Let $cmathcal{L}$ be a set of distinct positive integers whose largest element is $k$. The non-uniform set system $cbinom{[n]}{cmathcal{L}}$ consists of the subsets of $[n]$ whose…

Let $\mathscr K_{m_1,\ldots,m_n}^{3}$ be the complete multipartite 3-uniform hypergraph whose parts have sizes $m_1,\ldots,m_n$, and let $\lambda \mathscr K_{m_1,\ldots,m_n}^{3}$ d…