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Journal Articles Discrete Mathematics Year : 2018

Countable linear orders with disjoint infinite intervals are mutually orthogonal

Imed Zaguia
  • Function : Author

Abstract

Two linear orderings of a same set are perpendicular if the only self-mappings of this set that preserve them both are the identity and the constant mappings. Two linear orderings are orthogonal if they are isomorphic to two perpendicular linear orderings. We show that two countable linear orderings are orthogonal as soon as each one has two disjoint infinite intervals. From this and previously known results it follows in particular that each countably infinite linear ordering is orthogonal to itself

Dates and versions

hal-01816466 , version 1 (15-06-2018)

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Christian Delhommé, Imed Zaguia. Countable linear orders with disjoint infinite intervals are mutually orthogonal. Discrete Mathematics, 2018, 341 (7), pp.1885-1899. ⟨10.1016/j.disc.2018.03.011⟩. ⟨hal-01816466⟩
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