Countable linear orders with disjoint infinite intervals are mutually orthogonal

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
Document type :
Journal articles
Complete list of metadatas

http://hal.univ-reunion.fr/hal-01816466
Contributor : Réunion Univ <>
Submitted on : Friday, June 15, 2018 - 12:35:16 PM
Last modification on : Monday, September 2, 2019 - 9:43:10 AM

Identifiers

Collections

Citation

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

Share

Metrics

Record views

72