Faithful extensions on finite orders classes

Alain Guillet (1) , Jimmy Leblet (2) , Jean-Xavier Rampon (3)

1 UCL - Université Catholique de Louvain = Catholic University of Louvain
2 Laboratoire de Recherche Magellan
3 UN UFR ST - Université de Nantes - UFR des Sciences et des Techniques

In the particular case of finite orders, we investigate the notion of faithful extension among relations introduced in 1971 by R. Fraısse: 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.

Domaines: Mathématiques [math]

Alain Guillet, Jimmy Leblet, Jean-Xavier Rampon. Faithful extensions on finite orders classes. The Australasian Journal of Combinatorics, 2017, 69 (1), pp.1-17. ⟨hal-01625566⟩