  We consider the groundstate wavefunction of the quantum symmetric
antiferromagnetic XXZ chain with open and twisted boundary conditions at
$\Delta=-{1/2}$, along with the groundstate wavefunction of the corresponding
O($n$) loop model at $n=1$. Based on exact results for finite-size systems,
sums involving the wavefunction components, and in some cases the largest
component itself, are conjectured to be directly related to the total number of
alternating sign matrices and plane partitions in certain symmetry classes.
