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The study of the entanglement entropy and entanglement spectrum has proven to be very fruitful in identifying topological phases of matter. Typically, one performs numerical studies of finite-size systems. However, there are few rigorous results for finite-size systems. We revisit the problem of determining the rank of the "particle entanglement spectrum" of the Laughlin states. We reformulate the problem into a problem concerning the ideal of symmetric polynomials that vanish under thedoi:10.1088/1751-8113/48/28/285205 fatcat:3ne22fv4sjgrzctt2v6efvznpq