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Investigate lower and upper bounds for the maximum element in finite integer sets with distinct subset sums, providing analytical proofs and machine-checked formal verification.

August 20, 2026Open Access

On the Erdős Distinct Subset Sums Conjecture

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Investigate lower and upper bounds for the maximum element in finite integer sets with distinct subset sums, providing analytical proofs and machine-checked formal verification.
Applied discrete interval pigeonhole principles and boolean hypercube injections to establish total sum and element bounds.
Employed variance analysis on the boolean hypercube alongside the local central limit theorem to derive asymptotic lower bounds.
Formalized and machine-checked the mathematical proofs using the Lean 4 interactive theorem prover and Mathlib.
Established the exact total sum lower bound of at least 2^n - 1 and the exact maximum element lower bound of at least (2^n - 1)/n.
Re-derived the Erdős-Moser asymptotic bound of at least sqrt(2/pi) * (2^n / sqrt(n))(1 + o(1)) and surveyed upper bound constructions achieving values under 0.22096 * 2^n.
Achieved 100% machine-checked verification of the mathematical derivations within the Lean 4 proof assistant.

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Implication

Mathematical analysis demonstrates lower bounds and certified proofs for sets with distinct subset sums, clarifying exponential growth bounds in additive combinatorics.

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Charles EDOU NZE (2026) studied this question.

synapsesocial.com/papers/6a86b57f8a91293e6a1cce0b https://doi.org/10.5281/zenodo.21992092

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Implication

Mathematical analysis demonstrates lower bounds and certified proofs for sets with distinct subset sums, clarifying exponential growth bounds in additive combinatorics.

On the Erdős Distinct Subset Sums Conjecture

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Implication

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On the Erdős Distinct Subset Sums Conjecture

Key Points

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Implication

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