What does this research mean for the field?

The proofs of the Erdős-Heilbronn Conjecture, including exact sharpness on arithmetic progressions and Combinatorial Nullstellensatz derivations, can be fully formalized and machine-verified using the Lean 4 interactive theorem prover. Novelty: ClaimNovelty.CONFIRMATORY. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Provide a comprehensive mathematical analysis and interactive machine-checked verification of the Erdős-Heilbronn conjecture regarding lower bounds on restricted sumsets in prime cyclic groups.

August 29, 2026Open Access

Erdős-Heilbronn Restricted Sumset Conjecture

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CNCharles EDOU NZE

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Implication

Theoretical study establishes restricted sumset bounds in finite prime fields, demonstrating exact sharpness on arithmetic progressions.

Key Points

Provide a comprehensive mathematical analysis and interactive machine-checked verification of the Erdős-Heilbronn conjecture regarding lower bounds on restricted sumsets in prime cyclic groups.
Applied algebraic techniques via Alon's Combinatorial Nullstellensatz to non-vanishing bivariate polynomials over prime fields.
Analyzed exterior power actions and linear representations to assess restricted sumset expansion across finite abelian groups.
Engineered full machine-checked proofs of foundational base cases, reduction lemmas, and sharpness in the Lean 4 interactive theorem prover.
Demonstrated that the restricted sumset achieves the conjectured lower bound of min(p, 2|A| − 3) in prime fields, with exact equality 2k − 3 achieved on arithmetic progressions of length k.
Confirmed asymmetric subset expansions satisfying |A ^+ B| ≥ min(p, |A| + |B| − 2) whenever subset cardinalities differ.
Certified complete formal Lean 4 verification of arithmetic progression sharpness, Cauchy-Davenport reductions, and Nullstellensatz invariants with zero unproven assumptions or axioms.

Cite This Study

Charles EDOU NZE (2026) studied this question.

synapsesocial.com/papers/6a9299bb8e5d7d1fc0c11d0e https://doi.org/10.5281/zenodo.22132120

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Erdős-Heilbronn Restricted Sumset Conjecture

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Key Points

Cite This Study

Erdős-Heilbronn Restricted Sumset Conjecture

Discussion

Member takes

Implication

Key Points

Cite This Study

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