{"id":"openai-math/A-Counterexample-to-the-Infinite-Matroid-Packing-Covering-Conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/A-Counterexample-to-the-Infinite-Matroid-Packing-Covering-Conjecture-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-Counterexample-to-the-Infinite-Matroid-Packing-Covering-Conjecture-September-24-2026","tags":["infinite-matroids","matroid-theory","set-theory"],"score":0,"title":"A Counterexample to the Infinite Matroid Packing/Covering Conjecture","domain":"Combinatorics","family":"185","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Counterexamples to infinite matroid intersection and packing/covering"}