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Brignall, Robert
(2024).
DOI: https://doi.org/10.37236/12655
Abstract
The of permutation classes
and
is the class of all permutations formed by concatenations
, such that
is order isomorphic to a permutation in
, and
to a permutation in
. We give simple necessary and sufficient conditions on the classes
and
for their juxtaposition to be labelled well-quasi-ordered (lwqo): namely that both
and
must themselves be lwqo, and at most one of
or
can contain arbitrarily long zigzag permutations. We also show that every class without long zigzag permutations has a growth rate which must be integral.