4 problems

Let $b_4(n)$ denote the number of balanced $8\times 2n$ matrices. A linear recurrence of order $9$ with polynomial coefficients of degree $36$ should be satisfied by the sequence…

Determinant approximate-homomorphism conjecture. Under these hypotheses, the determinant is approximately additive on $A$ and $B$.

Fair-discrepancy propagation conjecture. If one fixed row has discrepancy less than $\epsilon$, then every row has discrepancy less than $\epsilon$.

Let $A\text{ }\in\mathcal{B}_{n}(\mathbb{R})$ be a square balanced matrix. An interior balanced-submatrix conjecture asserts that some interior of $A$, meaning a submatrix of $A$,…