5 problems

Let $\mathbb{S}$ be the parameter matrix of a $k$-transversal in a $d$-uniform $r$-regular hypergraph $\mathcal{G}$. Let $\xi$ be a $d$-th primitive root of unity. Characteristic-p…

For fixed parameters $q$, $b$, and $c$, call $(q,b,c)$ admissible if there is an integer $n_0=n_0(b,c;q)$ such that a $(b,c)$-coloring of $H(n,q)$ exists if and only if $n\geq n_0$…

Let $f: \{0,\ldots,q-1\}^n \rightarrow \{0,1\}$ be a function with $B$ zeros and $C$ ones, where $q\geq 3$. Suppose that for some $k$, every $k$-face has the same number … of ones…

Generalized correlation-immunity bound. If there exists a $(b,c)$-coloring in $H(n,q)$ with $b'+c'>q$, then

Classification conjecture. The set of perfect $k$-colorings of $\mathrm{Ci}_\infty(D_n)$ consists of perfect colorings induced from perfect colorings of the infinite path graph and…