Unformatted text preview: ² r k ³² n-1 r-k-1 ³ . Problem 22 (the number of partial derivatives) Let n i be the number oF derivatives taken oF the x i th variable. Then a total order oF n derivatives requires that these componentwise derivatives satisFy ∑ n i =1 n i = n , with n i ≥ 0. The number oF such is given by ² n + n-1 n-1 ³ = ² 2 n-1 n-1 ³ . Problem 23 (counting discrete wedges) We require that x i ≥ 1 and that they sum to a value less than k , i.e. n ± i =1 x i ≤ k ....
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- Winter '08
- Probability, Natural number, 1 MI, xi th variable