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Unformatted text preview: the right. Enumerate the number of ways to get by such steps from: (a) (0 , 0) to (1 , 2); (b) (0 , 0) to (2 , 3); (c) (0 , 0) to (4 , 2); and (d) (0 , 0) to (7 , 7). 3. For the chessboard labelled as in the preceding question, let a ( x,y ) denote the number of ways to get from (0 , 0) to the square labelled ( x,y ). Suppose x > and y > 0. Give a combinatorial proof that a ( x,y ) = a ( x1 ,y ) + a ( x,y1). 4. Let S = { 1 , 2 , 3 } . Below we describe various weight functions w for each subset T of S . In each case, write down the corresonding generating function. (a) w ( T ) is  T  (that is, the number of elements of T . (b) w ( T ) is the smallest number in T (if T = , then w ( T ) = 4). (c) w ( T ) is the sum of the elements of T (if T = , then w ( T ) = 0)....
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This note was uploaded on 06/12/2011 for the course CO 250 taught by Professor Guenin during the Spring '10 term at Waterloo.
 Spring '10
 GUENIN

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