2011/10/08 by Godbole, Anant, Lim, Chang Mou, Lyzinski, Vince +1
#05D40 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)
paper · doi:10.48550/arxiv.1110.1745
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=pn 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