4 problems

Divisibility conjecture. One has

Terminal-pattern divisibility conjecture. The following implications hold:

Possible-roots conjecture. For $M$, the rational roots of $w_l(M)$ lie in

Let $F_{2n+1}(x)$ be the generating polynomial for the odd-sized periodic ground state, and let ${\rm AHT}_{m}$ denote the corresponding alternating-sign-triangle sum rule. Odd per…