6 problems

Let $m$ be a positive integer, let $\varepsilon$ be an $m$-th primitive root of unity, and let $H(n,m)$ be the Hamming graph. Write $H_1,\dots,H_m$ for possibly empty induced subgr…

Sensitivity-weighted variable conjecture. For every Boolean function $f$,

Let $f$ be a Boolean graph property on the ${n \choose 2}$ possible edges. A min-term graph property is a graph property of the type defined in Chakraborty's work, and $f$ is non-t…

Let $f$ be a non-trivial graph property for graphs with $n$ vertices, so that $f$ is a Boolean function of the ${n \choose 2}$ possible edges. Turan's conjecture. The sensitivity s…

Nisan and Szegedy's Sensitivity Conjecture. There exist constants $c$ and $k$ such that for every Boolean function $f$,

Aaronson's lattice variant. There exist constants $c$ and $k$ such that for every non-trivial coloring $C$,