Every complex-weighted Eulerian orientation counting problem is either #P-hard or solvable in polynomial time with an NP oracle, giving the first comprehensive classification for #EO.
Complexity dichotomies for counting problems: Volume 1, Boolean domain
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The $\text{FP}^\text{NP}$ versus #P dichotomy for #EO
Every complex-weighted Eulerian orientation counting problem is either #P-hard or solvable in polynomial time with an NP oracle, giving the first comprehensive classification for #EO.