The Rotor Model and Combinatorics

We examine the groundstate wavefunction of the rotor model for different boundary conditions. Three conjectures are made on the appearance of numbers enumerating alternating sign matrices. In addition to those occurring in the O($n=1$) model we find the number $A_{\rm V}(2m+1;3)$, which 3-enumerates vertically symmetric alternating sign matrices.