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Graph Theory

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Homework is due 12pm Friday during the lecture. For Friday 23rd Jan please attempt questions 1,2,4,5,6. 1. Prove that if 0 ≤ a, k ≤ n then X k b=0  a b n − a k − b  =  n k  . (Recall that by definition c d  = 0 if d < 0 or c < d.) 2. Let m, n ≥ 1 be integers. Consider the paths starting from (0, 0) in Z 2 in which each step is from (a, b) to (a + 1, b) or from (a, b) to (a, b + 1) (i.e. at each step you move up or right by one). (i) Ho ...

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