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A Counterexample to the Infinite Matroid Packing/Covering Conjecture

OpenAI

OpenAI Mathopenai-math/A-Counterexample-to-the-Infinite-Matroid-Packing-Covering-ConjectureSep 24, 2026math.COAI-generatedscore 0

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.

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