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Q97 / 100
What is the Möbius function in combinatorics?
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Incorrect.
The correct answer is B) A function on posets μ(x,y) enabling Möbius inversion — the generalization of inclusion-exclusion and the number-theoretic Möbius function
B
Correct Answer
A function on posets μ(x,y) enabling Möbius inversion — the generalization of inclusion-exclusion and the number-theoretic Möbius function
Explanation
Möbius function μ on a poset: μ(x,x)=1, μ(x,y)=-Σ μ(x,z) for x≤z<y. Möbius inversion: f(x)=Σg(y) ↔ g(x)=Σ f(y)μ(y,x). Generalizes PIE; specializes to number-theoretic μ on divisibility poset.
Progress
97/100