7 problems

Let $n$ be the rank, and consider the circuit-rich pool instances generated by the source's recipe. Scale-invariant toy Rota Basis conjecture. For $n\in\{5,7,9,11,13\}$ and pool si…

Let $M$ be a rank-$7$ binary matroid instance from the circuit-rich pool template described in the source, including trap instances and conjugation by $\operatorname{GL}(7,2)$. Ran…

Let $M$ be a rank-$5$ binary matroid instance from the circuit-rich pool template described in the source, including trap instances and arbitrary conjugation by…

Let $alt(n)$ denote the alternating sequence of $0$s and $1$s of length $n$ that ends with $0$. Let $\d835\d835\mathcal{L}_n$ be the de Bruijn sequence obtained from the lexicograp…

Conjectural formula. For all $p\geq 3$ and $N\geq 0$,

Let $n\in{\mathbb N}$, let $\lambda$ be a partition of $n$, and let $U\in\operatorname{SYT}(\lambda)$ be such that the corresponding Novelli–Pak–Stoyanovskii algorithm is uniformly…

Let $n\in{\mathbb N}$, let $\lambda$ be a partition of $n$, and let $U,V\in\operatorname{SYT}(\lambda)$ be the standard Young tableaux defining the linear column-wise and linear ro…