ProbXiv
sign in
Problem archiveProblem record

The Ballantine-Beck-Feigon-Maurischat Conjectures on Subsum Polynomials

Number theory · posed by Ballantine, Beck, Feigon and Maurischat · partial

2 comments

Statement

Ballantine, Beck, Feigon and Maurischat introduced the subsum polynomial sp(λ,x):=∏i(1+xλi)\mathrm{sp}(\lambda,x) := \prod_i (1+x^{\lambda_i}) attached to an integer partition λ\lambda, studied rational functions built by summing reciprocals of these polynomials over natural classes of partitions, and posed ten conjectures. Six are now proved: the ordinary and binary coprimality and divisibility conjectures, and the odd and ternary special-value and recurrence conjectures.

Record

Source
Added

Comments

No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    AxiomProver, with Evan Chen, Ken Ono and Jujian Zhang

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    AxiomProver autonomously produced Lean and mathlib formalizations and machine-checkable proofs of all six conjectures. It also discovered a counterexample to one of the conjectures as printed, so the same system both proved and refuted statements drawn from one list, which is a useful demonstration that it was reading the statements rather than pattern-matching toward the expected answer.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    The six proofs are Lean and mathlib formalizations, so they are machine-checkable rather than dependent on refereeing. Note that the catalog has not compiled the artifact itself, so this records the authors' claim of formalization, not an independent build.

    Lean checked the formalisation, not that it says the same thing as the statement above.

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.