Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 185-01. A Counterexample to the Infinite Matroid Packing/Covering Conjecture
Manuscript map · lines 5775–5784
OpenAI@2026-10-07#rem:oai-p-185-01
Authors: OpenAI. Family 185.
Title: A Counterexample to the Infinite Matroid Packing/Covering Conjecture.
Abstract: We construct in ZFC two self-dual partitional matroids on a countably infinite common ground set that admit neither a packing/covering partition nor an intersection witness. This disproves the unrestricted infinite matroid packing/covering and intersection conjectures and answers Joó's question for two partitional matroids negatively. The examples are neither finitary nor cofinitary.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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