Preprint in the OpenAI Math release
A Counterexample to the Infinite Matroid Packing/Covering Conjecture
OpenAI
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.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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