Upper and lower bounds on the size of B_k[g] sets

2021/05/08 by Johnston, Griffin, Tait, Michael, Timmons, Craig
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.03706

Abstract

A subset A of the integers is a B_k[g] set if the number of multisets from A that sum to any fixed integer is at most g. Let F_k,g(n) denote the maximum size of a B_k[g] set in \1,…, n\. In this paper we improve the best-known upper bounds on F_k,g(n) for g>1 and k large. When g=1 we match the best upper bound of Green with an improved error term. Additionally, we give a lower bound on F_k,g(n) that matches a construction of Lindström while removing one of the hypotheses.

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