The matroid intersection conjecture

2026/07/09 by Dominic van der Zypen
Mathematics · #math.CO

paper · pdf

Abstract

We prove the matroid intersection conjecture, due to Nash-Williams \citeahaziv, for infinite matroids: If M_k = (E, \mathcal I_k) are matroids for k ∈ \0,1\, both having the same base set E, then there is J^* ∈ \mathcal I₀ ∩ \mathcal I₁ and disjoint subsets J_k⊆ J^* for k∈ \0,1\ such that cl_M0(J₀) ∪ cl_M1(J₁) = E.

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