The wpo characterization conjecture for strongly algebraic permutation classes

A permutation class is well-partially-ordered (wpo) if it has no infinite antichain under pattern containment. It is strongly algebraic if it and all of its subclasses have algebraic generating functions.

Strongly algebraic characterization conjecture. A permutation class is strongly algebraic if and only if it is wpo. The source proves that every strongly algebraic class is wpo and presents the converse as the author's conjecture; it says that little is known about strongly algebraic classes.