Arrangements of lines and pseudolines without adjacent triangles
Journal of Combinatorial Theory Series A
Symmetric matroid polytopes and their generation
European Journal of Combinatorics
Hi-index | 0.00 |
We discuss algorithmic steps when dealing with realizability problems in discrete geometry, especially that of finding realizations for a given oriented matroid. After a brief introduction to known methods, we discuss a dynamic inductive realization method, which has proven successful when other methods did not succeed. A useful theorem in this context in the rank 3 case asserts that a one-element extension of a uniform rank 3 oriented matroid depends essentially just on the mutations involving that element. There are problems in computational synthetic geometry of course, where intuition must help. In this context we mention the application of the software Cinderella to automated deduction in computational synthetic geometry, when studying face lattices of polytopes.