The independence number of a subset of an abelian group

2015/12/09 by Béla Bajnok, Bajnok, Béla, Imre Ruzsa +1
Mathematics · #11B75 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B75

paper · pdf · doi:10.48550/arxiv.1512.03037

arxiv created 2015/12/09 · arxiv updated 2015/12/10

Abstract

We call a subset A of the (additive) abelian group G \it t-independent if for all non-negative integers h and k with h+k ≤ t, the sum of h (not necessarily distinct) elements of A does not equal the sum of k (not necessarily distinct) elements of A unless h=k and the two sums contain the same terms in some order. A \it weakly t-independent set satisfies this property for sums of distinct terms. We give some exact values and asymptotic bounds for the size of a largest t-independent set and weakly t-independent set in abelian groups, particularly in the cyclic group \mathbb Z_n.

Related

• On the maximum size of a (k,l)-sum-free subset of an abelian group
• Sumsets with a minimum number of distinct terms
• The Maximum Size of (k,l)-Sum-Free Sets in Cyclic Groups
• Sum-free sets in abelian groups
• On unique sums in Abelian groups