An Experimental Study of Forbidden Patterns in Geometric Permutations by Combinatorial Lifting
Computational Geometry
2019-03-08 v1
Abstract
We study the problem of deciding if a given triple of permutations can be realized as geometric permutations of disjoint convex sets in . We show that this question, which is equivalent to deciding the emptiness of certain semi-algebraic sets bounded by cubic polynomials, can be "lifted" to a purely combinatorial problem. We propose an effective algorithm for that problem, and use it to gain new insights into the structure of geometric permutations.
Cite
@article{arxiv.1903.03014,
title = {An Experimental Study of Forbidden Patterns in Geometric Permutations by Combinatorial Lifting},
author = {Xavier Goaoc and Andreas Holmsen and Cyril Nicaud},
journal= {arXiv preprint arXiv:1903.03014},
year = {2019}
}