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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..
Antonio Montalbán. "Equimorphism invariants for scattered linear orderings." Fundamenta Mathematicae 191.2 (2006): 151-173. <http://eudml.org/doc/282788>.
@article{AntonioMontalbán2006, abstract = {
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..
}, author = {Antonio Montalbán}, journal = {Fundamenta Mathematicae}, keywords = {invariant; embeddability; scattered linear orderings; scattered equimorphism types}, language = {eng}, number = {2}, pages = {151-173}, title = {Equimorphism invariants for scattered linear orderings}, url = {http://eudml.org/doc/282788}, volume = {191}, year = {2006}, }
TY - JOUR AU - Antonio Montalbán TI - Equimorphism invariants for scattered linear orderings JO - Fundamenta Mathematicae PY - 2006 VL - 191 IS - 2 SP - 151 EP - 173 AB -
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..
LA - eng KW - invariant; embeddability; scattered linear orderings; scattered equimorphism types UR - http://eudml.org/doc/282788 ER -