Partition functions for states models on signed graphs

There are many models of physical systems based in unsigned graph theory, however there are some systems that cannot be modelled by unsigned graphs and that is the reason of signed graph states models. For these models, there are useful objects as partition functions, and systems that share these objects have some intrinsic properties in common, so it is interesting to build these models in order to relate those systems (with vertex switching invariance or equivalent knot invariance).
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