Characterizing partition functions of the vertex model
  We characterize which graph parameters are partition functions of a vertex model over an algebraically closed field of characteristic 0 (in the sense of de la Harpe and Jones). We moreover characterize when the vertex model can be taken so that its moment matrix has finite rank. 
Jan Draisma, Dion Gijswijt, L\'aszl\'o Lov\'asz, Guus Regts, Alexander   Schrijver
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