The open O(1) loop-model largest-component conjecture

Consider the dense O(1) loop model with open boundary conditions and system size $L$, and normalise its groundstate wavefunction so that its smallest element is $1$. Let $N_8(2n)$ count cyclically symmetric transpose-complement plane partitions and let $A_{\rm v}(2n-1)$ count vertically symmetric alternating sign matrices. The open-loop largest-component conjecture. The largest element of the wavefunction is $N_8(2n)$ for $L=2n$ and $A_{\rm v}(2n-1)$ for $L=2n-1$.

The O(1) loop model is the real loop counterpart of the corresponding XXZ chain, with loop fugacity $1$. The prediction links its extremal wavefunction component to symmetry classes of plane partitions and alternating sign matrices, and is supported only by the finite tables in the source.