Classification of Oriented Matroids

This page is dedicated to classification of oriented matroids, point configurations and polytopes.
The main feature of our classification is that it contains degenerate cases.

Classifications of oriented matroids w.r.t. the realizability (reorientation class)

You can download our classification results from the following links.
Each line of the files contains exactly one oriented matroid, reprensented by the RevLex-Index encoding of its chirotope,
which is used in the database of oriented matroids by Finschi and Fukuda.

Realizations of realizable oriented matroids

You can check realizability of the above realizable oriented matroids using the following realizations.
Realizations for OM(6,9) are not uploaded since one can check realizability of OM(6,9) easily from the result of OM(3,9).
If you would also like to get realizations for OM(6,9), please contact the authors.

Final polynomials of non-realizable oriented matroids

You can check non-realizability of the above non-realizable oriented matroids by looking at the following final polynomials.
Final polynomials for OM(6,9) are not uploaded since one can check non-realizabilty of OM(6,9) easily from the result of OM(3,9).
Please constact the authors if you would also like to get data of final polynomials for OM(6,9).

Combinatorial types of point configurations

You can download all possible combinatorial types of point configurations of fixed sizes from the following links.
We adopt the RevLex-Index encodings of chirotopes to represent combinatorial types.
Each line of the files contains exactly one combinatorial type.

Combinatorial types of polytopes

You can download all possible combinatorial types of polytopes of fixed sizes from the following links.
Each line of the file contains exactly one face lattice represented by the facet list,
where each bracket corresponds to facet.

Software

Software is available on request. If you would like the software, please contact the authors.

Links


Please feel free to contact the authors.
Hiroyuki Miyata (hmiyata AT is DOT s DOT u-tokyo DOT ac DOT jp)
Sonoko Moriyama (moriso AT dais DOT is DOT tohoku DOT ac DOT jp)
Komei Fukuda (fukuda AT ifor DOT math DOT ethz DOT ch)