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4204hw6 - 0 and suppose that the element x P covers only...

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Combinatorics II (MAD 4204) — Spring 2011 Due Wednesday 3/23/2011 Homework #6 Note: The midterm scheduled for March 30 has been canceled. Our final midterm will be on Wednesday, April 13. Final projects will be due on Wednesday, April 20. 1 Compute μ 13 2 45 68 7 , 13457 268 in the set partition lattice Π 8 . 2 Let P be a poset with a minimum element
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Unformatted text preview: 0, and suppose that the element x P covers only one other element, y . Prove that if y ˆ 0, then μ ˆ , x 0. 3 Consider the equation d n f d log n. Prove that there is a unique function that satisFes this equation, and that this function is given by f n log p if n is a power of the prime p , otherwise....
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