A complete dichotomy for complex-valued Holant^c

Understand

Holant problems are a family of counting problems on graphs, parametrised by sets of complex-valued functions of Boolean inputs.

• Holant^c denotes a subfamily of those problems, where any function set considered must contain the two unary functions pinning inputs to values 0 or 1.
• The complexity classification of Holant problems usually takes the form of dichotomy theorems, showing that for any set of functions in the family, the problem is either #P-hard or it can be solved in polynomial time.
• Previous such results include a dichotomy for real-valued Holant^c and one for Holant^c with complex symmetric functions.