Two linear orderings are equimorphic if they can be embedded in each other. We define invariants for scattered linear orderings which classify them up to equimorphism. Essentially, these invariants are finite sequences of finite trees with ordinal labels. Also, for each ordinal α, we explicitly describe the finite set of minimal scattered equimorphism types of Hausdorff rank α. We compute the invariants of each of these minimal types..
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-2-3,
author = {Antonio Montalb\'an},
title = {Equimorphism invariants for scattered linear orderings},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {151-173},
zbl = {1104.03040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-2-3}
}
Antonio Montalbán. Equimorphism invariants for scattered linear orderings. Fundamenta Mathematicae, Tome 189 (2006) pp. 151-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-2-3/