6 problems

Let $P_{\text{ASEP}}^{n}$ be the asymmetric subtour elimination polytope, let $\boldsymbol{x}$ be a vertex of this polytope, and let $\mathcal{N}(\boldsymbol{x})$ denote its neighb…

8-profile hardness conjecture. In direct analogy with the case of $\mathbb{S}_4$, these occurrences constitute the “hard case” for computing the $8$-profile.

Let $f^h(\mathrm{\textcircled{s}};a_1,\dots,a_k)$ denote the number of rational functions produced by a strategy $h$ for choosing valid multipliers in the decomposition of a consta…

Let $G=\mathbb{Z}_8^2$ and let a subset $S\subset G$ be primitive if it is not contained in a proper coset of a subgroup of $G$ and generates $G$. A subset is formally dual if ther…

Let $k\geq 10$ be an integer, and let $p$ and $q$ be integers satisfying $p\geq k+2$ and $q\geq k+1$. Write $r_k(p,q)$ for the smallest integer $n$ such that every red-blue colorin…

A rotor type is unboppy if it is neither palindromic nor block-repetitive, and a rotor has prime length when its length is a prime number. The compressor is the procedure discussed…