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Séminaire Lotharingien de Combinatoire, 84B.87 (2020), 12 pp.

# Lukas Kühne and Geva Yashfe

# Undecidability of *c*-Arrangement Matroid Representations

**Abstract.**
A *c*-arrangement is an arrangement of dimension-*c* subspaces such that all their sums have dimension a multiple of *c*. Matroids arising as normalized rank functions of *c*-arrangements are also known as multilinear matroids. We prove that there is no algorithm to decide whether a matroid is multilinear. In particular there is no algorithm to decide whether there exists a representable multiple of a given polymatroid.

Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.

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