Sets characterized by missing sums and differences

DOI10.1016/j.jnt.2011.05.003zbMath1261.11015arXiv0911.2292OpenAlexW2097610146MaRDI QIDQ640027

Yufei Zhao

Publication date: 12 October 2011

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.2292

zbMATH Keywords

difference setsum setMSTD

Mathematics Subject Classification ID

Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Additive bases, including sumsets (11B13) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (18)

Sets of Cardinality 6 Are Not Sum-dominant ⋮ Distribution of Missing Differences in Diffsets ⋮ Distribution of Missing Sums in Sumsets ⋮ Sum-dominant sets and restricted-sum-dominant sets in finite abelian groups ⋮ Infinite Families of Partitions into MSTD Subsets ⋮ MSTD sets and Freiman isomorphisms ⋮ Constructions of generalized MSTD sets in higher dimensions ⋮ Generalizing the distribution of missing sums in sumsets ⋮ On sets with more products than quotients ⋮ Fringe pairs in generalized MSTD sets ⋮ Generalized more sums than differences sets ⋮ Sums and differences of correlated random sets ⋮ When Sets Can and Cannot Have MSTD Subsets ⋮ When almost all sets are difference dominated in $\mathbb{Z}/n\mathbb{Z}$ ⋮ The bidirectional ballot polytope ⋮ Sets characterized by missing sums and differences in dilating polytopes ⋮ Union of Two Arithmetic Progressions with the Same Common Difference Is Not Sum-dominant ⋮ A geometric perspective on the MSTD question

Cites Work

• Counting MSTD sets in finite abelian groups
• Constructing MSTD sets using bidirectional ballot sequences
• Explicit constructions of infinite families of MSTD sets
• Constructing numerical semigroups of a given genus.
• On the number of sums and differences
• Additive completion and disjoint translations
• When almost all sets are difference dominated
• On A Conjecture of Conway
• A mean value density theorem of additive number theory
• Some explicit constructions of sets with more sums than differences
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