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  "problem_id": "vibemathed:defant-short-proofs-combinatorics",
  "title": "Conjectures of Hopkins, Sagan-Wilson and Defant et al. on Lattices, Parking Functions and the Plactic Monoid",
  "canonical_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.",
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      "title": "arXiv:2605.19979 - Short Proofs in Algebraic and Enumerative Combinatorics",
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      "attempted_at": "2026-05-19T00:00:00.000Z",
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