4204hw5 - 1 Prove that if x n≤ y in the poset P then...

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Combinatorics II (MAD 4204) — Spring 2011 Due Wednesday 3/2/2011 Homework #5 Note: The due date for this homework is also the date of Midterm #2. A linear extension of the poset P = ( X, ) is a linear order L on X such that x y (in P ) implies that x L y (in the linear extension). A set L of linear extensions of P realizes P if x y (in P ) if and only if x L y for every linear extension L ∈ L
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Unformatted text preview: . 1 Prove that if x n≤ y in the poset P , then there is a linear extension L of P in which y ≤ L x . 2 Prove that every Fnite poset has a realizing set of linear extensions. 3 Compute the M¨obius function for the poset P whose Hasse diagram appears below. Please express your answer as an upper-trangular matrix....
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