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Conference Papers Year : 2019

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

Abstract

We study the problem of deciding if a given triple of permutations can be realized as geometric permutations of disjoint convex sets in R^3. 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.
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Dates and versions

hal-02050539 , version 1 (07-03-2019)

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Xavier Goaoc, Andreas Holmsen, Cyril Nicaud. An experimental study of forbidden patterns in geometric permutations by combinatorial lifting. 35th International Symposium on Computational Geometry, 2019, Portland, United States. ⟨10.4230/LIPIcs.SoCG.2019.40⟩. ⟨hal-02050539⟩
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