Sharp Threshold Asymptotics for the Emergence of Additive Bases

Details Sharp Threshold Asymptotics for the Emergence of Additive Bases Sharp Threshold Asymptotics for the Emergence of Additive Bases

2011-10-08

arxiv.org/abs/1110.1745v3

Mathematics

Combinatorics

22 pages

Scientific paper

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

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