Faithful extension on finite order classes

Guillet, Alain;Leblet, Jimmy;Rampon, Jean-Xavier
(2017) The Australasian Journal of Combinatorics — Vol. 69 Part 1, n° 1, p. 1 (2017)

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  • Guillet, AlainUCLouvain
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  • Leblet, JimmyUniversité Jean Moulin Lyon 3
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  • Rampon, Jean-XavierUniversité de Nantes
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Abstract
In the particular case of finite orders, we investigate the notion of faithful extension among relations introduced in 1971 by R. Fraïssé: an order Q admits a faithful extension relative to an order P if P does not embed into Q and there exists a strict extension of Q into which P still does not embed. For most of the known order classes, we prove that if P and Q belong to a class then Q admits a faithful extension in this class. For the class of distributive lattices, we give an infinite family of orders P and Q such that P does not embed into Q and embeds in every strict extension of Q.
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Guillet, A., Leblet, J., & Rampon, J.-X. (2017). Faithful extension on finite order classes. The Australasian Journal of Combinatorics, 69 Part 1(1), 1. https://hdl.handle.net/2078.5/176125 (Original work published 2017)