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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