#p-hard refers to a class of problems that are at least as hard as the hardest problems in the complexity class #P, which is concerned with counting the number of solutions to decision problems. When a problem is classified as #p-hard, it means that if we could solve it efficiently, we could also efficiently count the solutions to any problem in #P. This connection implies that #p-hard problems are considered very challenging and are typically not solvable in polynomial time unless P = NP.
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