6 problems

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

Let ${\mathbb F}$ be a field, let $n$ and $k$ satisfy $1<k<n-1$, and consider the Grassmann graph of $k$-dimensional subspaces of ${\mathbb F}^n$ and its subgraph induced by the no…

In the setting of Boolean degree $d$ functions on Grassmann graphs and the constant-depth decision-tree conjecture, the depth of the decision tree is the quantity under considerati…

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…

Let $H$ be the vector space underlying a sesquilinear form, and let $k$ be such that the associated dimension satisfies the exceptional case $\dim H=2k$. The relevant transformatio…

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…