A Blueprint for the Formalization of Seymour's Matroid Decomposition Theorem
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909980972548096 |
|---|---|
| author | Sergeev, Ivan Dvorak, Martin Rampell, Cameron Sandey, Mark Monticone, Pietro |
| author_facet | Sergeev, Ivan Dvorak, Martin Rampell, Cameron Sandey, Mark Monticone, Pietro |
| contents | 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 $R_{10}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01255 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Blueprint for the Formalization of Seymour's Matroid Decomposition Theorem Sergeev, Ivan Dvorak, Martin Rampell, Cameron Sandey, Mark Monticone, Pietro Combinatorics 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 $R_{10}$. 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. |
| title | A Blueprint for the Formalization of Seymour's Matroid Decomposition Theorem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.01255 |