4203hw5 - and 3? 3 How many permutations of [ n ] are there...

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Combinatorics (MAD 4203) — Fall 2010 Due Wednesday 10/27 Homework #5 1 Suppose that n is a multiple of 3. Prove that c ( n, n / 3 ) n ! 3 n / 3 ( n / 3 )! . (Here c ( n, k ) is a signless Stirling number of the Frst kind, i.e., it counts the number of permutations of n with k cycles.) 2 How many two-digit positive integers are relatively prime to both 2
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Unformatted text preview: and 3? 3 How many permutations of [ n ] are there in which at least one of the Frst two entries is even? 4 How many permutations of [ n ] contain exactly one cycle of length 1? 5 ind an explicit formula for a n if a = 1 and a n +1 = 3 a n + 2 n for all n 0....
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