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The quasiholes of the Read-Rezayi clustered quantum Hall states areconsidered, for any number of particles and quasiholes on a sphere, and for anydegree k of clustering. A set of trial wavefunctions, that are zero-energyeigenstates of a k+1-body interaction, and so are symmetric polynomials thatvanish when any k+1 particle coordinates are equal, is obtained explicitly andproved to be both complete and linearly independent. Formulas for the number ofstates are obtained, without the use of (but in agreement with) conformal fieldtheory, and extended to give the number of states for each angular momentum. Aninteresting recursive structure emerges in the states that relates those for kto those for k-1. It is pointed out that the same numbers of zero-energy statescan be proved to occur in certain one-dimensional models that have recentlybeen obtained as limits of the two-dimensional k+1-body interactionHamiltonians, using results from the combinatorial literature.Comment: 9 pages. v2: minor corrections; additional references; note added on  connection with one-dimensional Hamiltonians of recent interes

Wavefunctions and counting formulas for quasiholes of clustered quantum Hall states on a sphere