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Journal Articles Journal of Computational Geometry Year : 2021

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 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.

Dates and versions

hal-03152958 , version 1 (25-02-2021)

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