Formalizing the Excluded Minor Characterization of Binary Matroids in the Lean Theorem Prover

Abstract

A matroid is a mathematical object that generalizes the notion of linear independence of a set of vectors to an abstract independence of sets, with applications to optimization, linear algebra, graph theory, and algebraic geometry. Matroid theorists are often concerned with representations of matroids over fields. Tutte's seminal theorem proven in 1958 characterizes matroids representable over GF(2) by noncontainment of U2,4 as a matroid minor. In this thesis, we document a formalization of the theorem and its proof in the Lean Theorem Prover, building on its community-built mathematics library, mathlib.