  Certain well known quantum Hall states -- including the Laughlin states, the
Moore-Read Pfaffian, and the Read-Rezayi Parafermion states -- can be defined
as the unique lowest degree symmetric analytic function that vanishes as at
least p powers as some number (g+1) of particles approach the same point.
Analogously, these same quantum Hall states can be generated as the exact
highest density zero energy state of simple angular momentum projection
operators. Following this theme we determine the highest density zero energy
state for many other values of p and g.
