Faithful extensions on finite orders classes

Abstract : 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.
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The Australasian Journal of Combinatorics, Combinatorial Mathematics Society of Australasia (Inc.), 2017, 69 (1), pp.1-17
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Dernière modification le : mardi 31 octobre 2017 - 01:04:00

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Alain Guillet, Jimmy Leblet, Jean-Xavier Rampon. Faithful extensions on finite orders classes. The Australasian Journal of Combinatorics, Combinatorial Mathematics Society of Australasia (Inc.), 2017, 69 (1), pp.1-17. 〈hal-01625566〉

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