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.

The following versions are available: