2 problems

Mills–Robbins–Rumsey's refined vertical-symmetry conjecture. The number of $b\in\TSPP{2n+1}$ satisfying $\gamma(b)=b$ and $U_2(b)=r-1$ should equal the number of vertically symmetr…

Let $A_n(z,\rho):=A_n(z,\rho,1)$, and for odd order define … where $\operatorname{HSASM}(2m+1)$ is the set of horizontally symmetric ASMs of order $2m+1$, $\mu(A)$ is the statistic…