Record Compositions of Alternating Permutations

Precise statement

Amdeberhan, Shareshian and Stanley showed a function from the theory of partition Eisenstein series counts alternating permutations with a given record partition, and asked whether a similar theory exists for record compositions, suggesting a role for noncommutative symmetric functions. The paper solves that open problem with a product formula.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

AxiomProver

The paper states that AxiomProver autonomously produced and verified the results in Lean, and devotes a section to the protocol, the formal files and the verification environment.

Provider: unknown · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

The paper reports an accompanying Lean/mathlib formalization produced autonomously by AxiomProver, described in its own section. Not rebuilt here, and not independently reviewed. Preprint, not refereed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-07-14

   arXiv

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.