Semidefinite Functions on Categories

László Lovász, Alexander Schrijver


Freedman, Lovász and Schrijver characterized graph parameters that can be represented as the (weighted) number of homomorphisms into a fixed graph. Several extensions of this result have been proved. We use the framework of categories to prove a general theorem of this kind. Similarly as previous resuts, the characterization uses certain infinite matrices, called connection matrices, which are required to be positive semidefinite.

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