Conjectures of Hopkins, Sagan-Wilson and Defant et al. on Lattices, Parking Functions and the Plactic Monoid
Statement
A collection of open problems from the algebraic and enumerative combinatorics literature, resolved in one paper: a conjecture of Defant, Jiang, Marczinzik, Segovia, Speyer, Thomas and Williams on the echelonmotion operator on modular lattices, which also yields a new algebraic bijective proof of Dilworth's theorem; conjectures of Hopkins on parking function statistics studied by Stanley and Yin; and two conjectures of Sagan and Wilson on centralizers in the plactic monoid.
Record
Comments
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proof attempt · #1
ChatGPT 5.4 Pro, with Colin DefantThe 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.
The claim is unusually flat: all of these proofs were obtained autonomously by ChatGPT 5.4 Pro. The author's role was selecting the problems and writing them up. Worth noting that the first conjecture settled is one the author himself co-posed, so this is a mathematician using a model to close his own open problem.
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