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Dec 6, 2022 at 9:48 comment added Emil Jeřábek A much simpler example are perfect matchings in bipartite graphs: one can decide in polynomial time if such a matching exists, but counting them is #P-complete (this is the same as computing the permanent of $\{0,1\}$-matrices).
Dec 6, 2022 at 7:54 history answered Per Alexandersson CC BY-SA 4.0