Name
Abstract | ||
|---|---|---|
A subset A of {0,1,...,n} is said to be a 2-additive basis for {1,2,...,n} if each j in {1,2,...,n} can be written as j=x+y, x,y in A, x<=y. If we pick each integer in {0,1,...,n} independently with probability p=p_n tending to 0, thus getting a random set A, what is the probability that we have obtained a 2-additive basis? We address this question when the target sum-set is [(1-alpha)n,(1+alpha)n] (or equivalently [alpha n, (2-alpha) n]) for some 0<alpha<1. Under either model, the Stein-Chen method of Poisson approximation is used, in conjunction with Janson's inequalities, to tease out a very sharp threshold for the emergence of a 2-additive basis. Generalizations to k-additive bases are then given. |
Year | Venue | Keywords |
|---|---|---|
2013 | Integers | number theory |
Field | DocType | Volume |
Integer,Discrete mathematics,Combinatorics,Generalization,Poisson distribution,Asymptotic analysis,Mathematics | Journal | 13 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Anant P. Godbole | 1 | 95 | 16.08 |
| chang mou lim | 2 | 0 | 0.34 |
| vince lyzinski | 3 | 64 | 8.93 |
| Nicholas George Triantafillou | 4 | 0 | 0.34 |