Almost all matroids are nonrepresentable

By P. Nelson. 2016

60 citations recorded by the source corpus.

We prove that, as n tends to infinity, the proportion of n ‐element matroids that are representable tends to zero.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a55df468daeaa247b29ceeb834cfae4b04e94ff8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Federico Ardila
2. June Huh
3. Graham C. Denham
4. Nicholas Proudfoot
5. Jacob P. Matherne
6. Botong Wang
7. Tom Braden
8. Eric Katz

In Discrete Mathematics and Combinatorics

1. Federico Ardila
2. June Huh
3. Graham C. Denham
4. Botong Wang
5. Nicholas Proudfoot
6. Jacob P. Matherne
7. Tom Braden
8. Eric Katz

In Geometry and Topology

1. Federico Ardila
2. June Huh
3. Graham C. Denham
4. Botong Wang
5. Nicholas Proudfoot
6. Tom Braden
7. Jacob P. Matherne
8. Eric Katz

Citations in the corpus

• COMBINATORIAL APPLICATIONS OF THE HODGE–RIEMANN RELATIONS (2017, background): “cond is realizable over kif and only if the characteristic of kis not 2, and the third is not realizable over any field. It was recently shown that almost all matroids are not realizable over any field [43]. Definition 10. We introduce variables x F, one for each nonempty proper flat Fof M, and consider”
• A semi-small decomposition of the Chow ring of a matroid (2020, background): “Almost all matroids are not realizable over any field [24].”
• Lagrangian geometry of matroids (2020, background): “ver a field F if there exists a linear subspace V —FE such that S—Eis independent in M if and only if the projection from V to FS is surjective. Almost all matroids are not representable over any field [Nel18]. 8 FEDERICO ARDILA, GRAHAM DENHAM, AND JUNE HUH their solution typically requires a fundamen”