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# An experimental study of forbidden patterns in geometric permutations by combinatorial lifting

1 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : We study the problem of deciding if a given triple of permutations can be realized as geometric permutations of disjoint convex sets in R3. 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. In particular, we prove that all triples of permutations of size 5 are realizable, and give a complete list of triples of size 6 that are not.
Document type :
Journal articles
Domain :

https://hal.inria.fr/hal-03152958
Contributor : Xavier Goaoc Connect in order to contact the contributor
Submitted on : Thursday, February 25, 2021 - 10:58:18 PM
Last modification on : Friday, April 1, 2022 - 3:45:48 AM

### Citation

Xavier Goaoc, Andreas Holmsen, Cyril Nicaud. An experimental study of forbidden patterns in geometric permutations by combinatorial lifting. Journal of Computational Geometry, Carleton University, Computational Geometry Laboratory, 2021, Special Issue of Selected Papers from SoCG 2019, 11 (2), pp.131-161. ⟨10.20382/jocg.v11i2a6⟩. ⟨hal-03152958⟩

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