4 problems

Let $V=\mathbb{F}_q^n$ and let $J_q(n,k)$ be the Grassmann graph whose vertices are the $k$-dimensional subspaces of $V$. A function $f$ on the vertices is Boolean degree $1$ if it…

Let $J_q(n,k)$ be the Grassmann graph on the $k$-dimensional subspaces of an $n$-dimensional vector space over the finite field of order $q$. A Boolean degree $d$ function is a Boo…

Grassmann eigenvalue conjecture. (i) If $(n,q) eq (2d,2)$, then

Eventual Grassmann graph classification conjecture. Let $q$ be a prime power. Then there exists a constant $n_q$ such that a Boolean degree $1$ function on $J_q(n,k)$ is trivial fo…