An inverse theorem for the restricted set addition in Abelian groups.

DOI10.1016/j.jalgebra.2005.04.021zbMath1095.11046OpenAlexW2005815733MaRDI QIDQ2386056

Gyula Károlyi

Publication date: 22 August 2005

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: http://cds.cern.ch/record/858908

zbMATH Keywords

Abelian groupsarithmetic progressionsnumbers of elementsCombinatorial Nullstellensatz

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Other combinatorial number theory (11B75) Abelian groups (20K99) Inverse problems of additive number theory, including sumsets (11P70)

Related Items

Linear extension of the Erdős-Heilbronn conjecture, Permutations, hyperplanes and polynomials over finite fields, On the exterior algebra method applied to restricted set addition, Some remarks on barycentric-sum problems over cyclic groups, A generalization of sumsets modulo a prime, Permutations over cyclic groups, Restricted set addition: the exceptional case of the Erdős-Heilbronn conjecture, A Step Beyond Kemperman's Structure Theorem, On the critical pair theory in abelian groups: beyond Chowla's theorem, A compactness argument in the additive theory and the polynomial method.

Cites Work

• On small sumsets in an abelian group
• Orthogonal pairings of Euclidean spaces
• Sumsets in vector spaces over finite fields
• Rectification principles in additive number theory
• Optimally small sumsets in finite abelian groups.
• The Erdős-Heilbronn problem in Abelian groups.
• The polynomial method and restricted sums of congruence classes
• Restricted set addition in groups. II: A generalization of the Erdős-Heilbronn conjecture
• A compactness argument in the additive theory and the polynomial method.
• Abschätzung der asymptotischen Dichte von Summenmengen
• On Restricted Sums
• The Critical Pairs of Subsets of a Group of Prime Order
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• Combinatorial Nullstellensatz
• Cyclic Spaces for Grassmann Derivatives and Additive Theory
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• Restricted Set Addition in Groups I: The Classical Setting
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• Restricted sums of cardinality \(1+p\) in a vector space over \(\mathbb{F}_p\)
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