What does this research mean for the field?

The Erdős-Heilbronn Conjecture and its associated combinatorial and algebraic proofs can be fully formalized and machine-verified using the Lean 4 interactive theorem prover. Novelty: ClaimNovelty.CONFIRMATORY. Consensus alignment: ConsensusAlignment.SUPPORTS_CONSENSUS.

What question did this study set out to answer?

To provide an exhaustive theoretical analysis and complete formal verification of the Erdős-Heilbronn restricted sumset conjecture in additive combinatorics.

August 29, 2026Open Access

Erdős-Heilbronn Restricted Sumset Conjecture

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Authors

CNCharles EDOU NZE

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Implication

Theoretical analysis demonstrates sharp lower bounds and machine-checked proofs for restricted sumsets in prime fields, highlighting rigorous algebraic verification.

Key Points

To provide an exhaustive theoretical analysis and complete formal verification of the Erdős-Heilbronn restricted sumset conjecture in additive combinatorics.
Applied the Combinatorial Nullstellensatz via non-vanishing coefficient criteria to bivariate polynomials over cyclic prime fields.
Synthesized exterior algebra actions and Hamidoune minimal invariants to characterize restricted sumset expansions across abelian groups.
Executed machine-checked formalization in Lean 4 and Mathlib with zero external axioms and zero sorry placeholders.
Derived exact sharpness for arithmetic progressions of size k, yielding a minimal restricted sumset size of 2k − 3.
Established lower bounds of min(p, |A| + |B| − 2) for asymmetric restricted sumsets where subset sizes differ.
Achieved 100% formal verification of base cases, Cauchy-Davenport reductions, and Nullstellensatz invariants without linter warnings.

Cite This Study

Charles EDOU NZE (2026) studied this question.

synapsesocial.com/papers/6a92be7b8e5d7d1fc0c123d1 https://doi.org/10.5281/zenodo.22132121

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Implication

Theoretical analysis demonstrates sharp lower bounds and machine-checked proofs for restricted sumsets in prime fields, highlighting rigorous algebraic verification.

Erdős-Heilbronn Restricted Sumset Conjecture

Discussion

Member takes

Implication

Key Points

Cite This Study

Erdős-Heilbronn Restricted Sumset Conjecture

Discussion

Member takes

Implication

Key Points

Cite This Study

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