4 problems

Let $b(d)$ be defined by … where $a(n)$ is the sequence specified in the paper. For a graph $G$, let $\operatorname{bp}_2(G)$ be the least number of bipartite cliques in a $2$-cove…

Let $a(n)$ be the non-decreasing list of all positive integers except $1$, with each number $3\cdot2^r$ repeated twice, and define … Let $n(2,d)$ denote the maximum number of pairw…

Let $n(0,d)=1$ for all $d\geqslant1$, and for $1\leqslant k\leqslant d$ let $n(k,d)$ be the maximum number of pairwise $k$-neighborly boxes in $\mathbb{R}^d$. Pascal-type conjectur…

Let $n(2,d)$ denote the maximum number of pairwise $2$-neighborly axis-aligned boxes in $\mathbb{R}^d$, and let the construction in the paper produce a lower bound for this quantit…