Counting MSTD Sets in Finite Abelian Groups
arXiv:0911.2288 · doi:10.1016/j.jnt.2010.06.001
Abstract
In an abelian group G, a more sums than differences (MSTD) set is a subset A of G such that |A+A|>|A-A|. We provide asymptotics for the number of MSTD sets in finite abelian groups, extending previous results of Nathanson. The proof contains an application of a recently resolved conjecture of Alon and Kahn on the number of independent sets in a regular graph.
17 pages
References in corpus (6)
- The Number of Independent Sets in a Regular Graph
- Constructing MSTD Sets Using Bidirectional Ballot Sequences
- Sets Characterized by Missing Sums and Differences
- Some explicit constructions of sets with more sums than differences
- The number of independent sets in a graph with small maximum degree
- Explicit constructions of infinite families of MSTD sets
Cited by in corpus (6)
- Constructing MSTD Sets Using Bidirectional Ballot Sequences
- The Bipartite Swapping Trick on Graph Homomorphisms
- Sets Characterized by Missing Sums and Differences
- Entropies of weighted sums in cyclic groups and an application to polar codes
- Sets of Cardinality 6 Are Not Sum-dominant
- On the computational complexity of MSTD sets