T1 - Problem 1: Give a combinatorial proof of the identity...

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Unformatted text preview: Problem 1: Give a combinatorial proof of the identity n+m k Problem 2: k m i = i=0 n k−i Give a combinatorial proof of the identity n 3n = k=0 nk 2. k Problem 3: Let an,k be the number of subsets of {1, . . . , n} of size k that contains no consecutive pairs (i.e. i and i + 1 form a consecutive pair for any i = 1, . . . , n − 1). Give a combinatorial proof that an,k = Problem 4: n−k+1 . k Give a combinatorial proof to the identity k ≥0 n 2k = k≥0 n . 2k + 1 Problem 5: Let S be the set of all subset of {1, 2, 4, 6, 7} of size two . Define w(A) = (a − b)2 = (b − a)2 where A = {a, b} ∈ S . Write the generating function of S with respect to this weight. 1 ...
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This note was uploaded on 11/26/2011 for the course MATH 239 taught by Professor M.pei during the Spring '09 term at Waterloo.

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