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Glossary

RevLex-Index

For a given number of elements $$n and a given rank $$r of elements, the RevLex-Index uniquely identifies isomorphism classes of oriented matroids, or abstract order types, or abstract dissection types with $$n elements of rank $$r. 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 .

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}.