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The undecidability of joint embedding for 3-dimensional permutation classes
Discrete mathematics & theoretical computer science, Permutation Patterns 2019, Tome 22 (2020-2021) no. 2.

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As a step towards resolving a question of Ru\v{s}kuc on the decidability of joint embedding for hereditary classes of permutations, which may be viewed as structures in a language of 2 linear orders, we show the corresponding problem is undecidable for hereditary classes of structures in a language of 3 linear orders. 
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     title = {The undecidability of joint embedding for 3-dimensional permutation classes},
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Braunfeld, Samuel. The undecidability of joint embedding for 3-dimensional permutation classes. Discrete mathematics & theoretical computer science, Permutation Patterns 2019, Tome 22 (2020-2021) no. 2. doi : 10.46298/dmtcs.6165. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6165/

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