All Questions
1
question
0
votes
0
answers
42
views
Upper bound of number of k-tuples whose components are non-negative integers and sum up to n?
Is there any nontrivial upper bound for the size of $\{(x_1,\dots,x_k)\in\mathbb{N}^k:\sum_{i=1}^kx_i=n\}?$ We may assume $k,n$ are large enough but $k\ll n$, so an asymptotic bound is also helpful.
- 2,075