2 Answered Questions for the topic Partitions

12/21/20

Prove that among all the 2^(n−1) compositions of n, the part k occurs a total of (n − k + 3)2^(n−k−2) times

Let 1 ≤ k < n. Prove that among all the 2n−1compositions of n, the part k occurs a total of (n − k + 3)2n−k−2 times. For instance, if n = 4 and k = 2, then the part 2 appears once in 2 + 1 + 1,... more
Partitions Mathematics

07/26/17

Please explain to me the workings of this formula: P(n) ~ pi√3 exp (pi √2n/3) Thank you!

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