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arXiv · 2607.08802

The matroid intersection conjecture

Dominic van der Zypen
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Abstract

We prove the matroid intersection conjecture, due to Nash-Williams \cite{ahaziv}, for infinite matroids: If $M_k = (E, {\mathcal I}_k)$ are matroids for $k \in \{0,1\}$, both having the same base set $E$, then there is $J^* \in {\mathcal I}_0 \cap {\mathcal I}_1$ and disjoint subsets $J_k\subseteq J^*$ for $k\in \{0,1\}$ such that $\text{cl}_{M_0}(J_0) \cup \text{cl}_{M_1}(J_1) = E$.

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Dominic van der Zypen. 2026-07-15. The matroid intersection conjecture. https://arxiv.org/abs/2607.08802

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