Home | Catalog of Oriented Matroids | Catalog of Point Configurations | Catalog of Hyperplane Arrangements | Glossary |

RevLex-Index

For a given rank r and a given number n of
elements, the RevLex-Index uniquely
identifies isomorphism classes of
oriented matroids, or
abstract order types, or
abstract dissection types
of rank r with n elements.
The index is based on the representation of oriented matroids by chirotopes,
where the signs of the bases are ordered in *reverse lexicographic*
order, and the representative is the oriented matroid in the corresponding
equivalence class with lexicographically maximal chirotope, where
- < + < 0.

The ordering of the isomorphism classes of oriented matroids is by lexicographical increasing representative.

The ordering of the abstract order types is by the (RevLex-Index of the) isomorphism class and (inside one ismorphism class of oriented matroids) by lexicographical increasing representative.

The ordering of the abstract dissection types is by the (RevLex-Index of the) isomorphism class and (inside one ismorphism class of oriented matroids) by lexicographical increasing representative; the infinity element is the last element n in the ground set E = {1,..,n}.

Maintained by Lukas Finschi (finschi [at] ifor.math.ethz.ch)