A note on the order type of minoring orderings and some algebraic properties of ω2-well quasi-orderings

• Published in: 2014 XL Latin American Computing Conference (CLEI) pp. 1 - 9
• Main Authors: Abriola, Sergio, Figueira, Santiago
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-09-2014
• Subjects: Automata; Barium; Computer science; Electronic mail; Inspection; Quality of service; Upper bound
• DOI: 10.1109/CLEI.2014.6965188

The minoring ordering between finite sets of (X,≤) is a well quasi-ordering provided (X,≤) is an ω 2 -well quasi-ordering. We mention some known facts about ω 2 -well quasi orderings, and we prove some new results about them. We also study some algebraic properties of the minoring well-quasi ordering over finite sets of (X, ≤), such as the behaviour of its order type when the underlying set is a disjoint sum, and give a tight lower bound for its maximal order type in terms of the maximal order type of (X,≤). We also state some observations regarding the upper bound.