{"date_created":"2026-03-04T12:09:26Z","type":"preprint","_id":"21400","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"publication":"arXiv","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"page":"18","year":"2026","arxiv":1,"OA_place":"repository","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","doi":"10.48550/arXiv.2601.01255","language":[{"iso":"eng"}],"publication_status":"submitted","day":"03","related_material":{"link":[{"relation":"supplementary_material","url":"https://ivan-sergeyev.github.io/seymour/blueprint.pdf"}]},"citation":{"short":"I. Sergeev, M. Dvorak, C. Rampell, M. Sandey, P. Monticone, ArXiv (n.d.).","apa":"Sergeev, I., Dvorak, M., Rampell, C., Sandey, M., &#38; Monticone, P. (n.d.). A blueprint for the formalization of Seymour’s matroid decomposition theorem. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2601.01255\">https://doi.org/10.48550/arXiv.2601.01255</a>","ieee":"I. Sergeev, M. Dvorak, C. Rampell, M. Sandey, and P. Monticone, “A blueprint for the formalization of Seymour’s matroid decomposition theorem,” <i>arXiv</i>. .","ama":"Sergeev I, Dvorak M, Rampell C, Sandey M, Monticone P. A blueprint for the formalization of Seymour’s matroid decomposition theorem. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2601.01255\">10.48550/arXiv.2601.01255</a>","mla":"Sergeev, Ivan, et al. “A Blueprint for the Formalization of Seymour’s Matroid Decomposition Theorem.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2601.01255\">10.48550/arXiv.2601.01255</a>.","ista":"Sergeev I, Dvorak M, Rampell C, Sandey M, Monticone P. A blueprint for the formalization of Seymour’s matroid decomposition theorem. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2601.01255\">10.48550/arXiv.2601.01255</a>.","chicago":"Sergeev, Ivan, Martin Dvorak, Cameron Rampell, Mark Sandey, and Pietro Monticone. “A Blueprint for the Formalization of Seymour’s Matroid Decomposition Theorem.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2601.01255\">https://doi.org/10.48550/arXiv.2601.01255</a>."},"status":"public","abstract":[{"lang":"eng","text":"This document is a blueprint for the formalization in Lean of the structural theory of regular matroids underlying Seymour's decomposition theorem. We present a modular account of regularity via totally unimodular representations, show that regularity is preserved under 1-, 2-, and 3-sums, and establish regularity for several special classes of matroids, including graphic, cographic, and the matroid R10. The blueprint records the logical structure of the proof, the precise dependencies between results, and their correspondence with Lean declarations. It is intended both as a guide for the ongoing formalization effort and as a human-readable reference for the organization of the proof."}],"date_updated":"2026-03-09T15:14:18Z","external_id":{"arxiv":["2601.01255"]},"title":"A blueprint for the formalization of Seymour's matroid decomposition theorem","date_published":"2026-01-03T00:00:00Z","corr_author":"1","month":"01","article_processing_charge":"No","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2601.01255"}],"author":[{"full_name":"Sergeev, Ivan","orcid":"0009-0004-9145-8785","first_name":"Ivan","id":"ca3c9187-9a72-11ee-a009-8af825d896b0","last_name":"Sergeev"},{"full_name":"Dvorak, Martin","orcid":"0000-0001-5293-214X","first_name":"Martin","last_name":"Dvorak","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425"},{"last_name":"Rampell","full_name":"Rampell, Cameron","first_name":"Cameron"},{"full_name":"Sandey, Mark","first_name":"Mark","last_name":"Sandey"},{"last_name":"Monticone","first_name":"Pietro","full_name":"Monticone, Pietro"}]}