7 problems

Let $u_\mathbb{P}(q;n)$ be the counting quasipolynomial for nonattacking configurations of $q$ copies of a two-move rider $\mathbb{P}$ on the dilated unit board, and let…

Let $\mathbb P$ be a piece, and let a twisted Fibonacci spiral be the vertex configuration defined by four selected moves of $\mathbb P$ in the Fibonacci-spiral pattern, together w…

Let $F_q$ be the $q$th Fibonacci number and let $[F_q]=\{1,2,\ldots,F_q\}$. For the inside-out polytope associated with $q$ queens, let $D$ denote its denominator. Queen denominato…

Let $F_q$ be the $q$th Fibonacci number, let $[F_q]=\{1,2,\ldots,F_q\}$, and let $u_{\mathbb Q}(q;n)$ be the counting quasipolynomial for $q$ queens. Kotěšovec's conjecture. The pe…

Bishop-and-knight checkmate move-count conjecture. From the worst possible starting configuration that permits a forced win, checkmate requires about

Legal-diagram count conjecture. The number $N$ of legal diagrams in the game of chess without promotions satisfies

Let $F_q$ be the $q$th Fibonacci number, and consider vertex configurations of $q$ queens in the square-board inside-out polytope. Queen maximal-denominator conjecture. The largest…