Unformatted text preview: + 1 and so D I [I n! n! ()n+l] ( 1 1 1 ()n 1 ) n = n. n. 2! + 3! ... + 1 = n! 1 I! + 2! 3! + . .. + 1 n! as required. 10. (a) [BB] Using Proposition 7.6.2, Dn = n! n! + [n(n 1)(n  2) . . ·3] [n(n 1)(n  2) ... 4] + . .. + (Itl n + (_I)n = n[ (n  1) (n  2) ... 3 (n  1) (n  2) ... 4 + . .. + (1) nl (n  1) 1 + ( 1) n == (_I)n (mod n). (b) [BB] This follows immediately from part (a). 11. (a) [BB] (n 1)(D n  l + D n  2 ) = (n 1) { (n I)! [1 ~ + ~  ... + (1 tl 1 ] I! 2! (n I)! +(n2)![I~+~"'+(I)n2 1 ]} I! 2! (n 2)! =n(nl)![I~+~"'+(ltl 1 ] I! 2! (n I)! (n I)! [1 ~ + ~  ... + (1 tl 1 ] I! 2! (n I)! +(nl)![I~+~"'+(lt2 1 ] I! 2! (n 2)! = n!(I~ + ~  ... + (lt~) n!(lt~ (n 1)!(ltl 1 I! 2! n! n! (n  I)! = Dn (I)n (_I)nl = Dn...
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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