  We take the first steps in developing a theory of transport of patterns from
Fishburn permutations to (modified) ascent sequences. Given a set of pattern
avoiding Fishburn permutations, we provide an explicit construction for the
basis of the corresponding set of modified ascent sequences. Our approach is in
fact more general and can transport patterns between permutations and
equivalence classes of so called Cayley permutations. This transport of
patterns relies on a simple operation we call the Burge transpose. It operates
on certain biwords called Burge words. Moreover, using mesh patterns on Cayley
permutations, we present an alternative view of the transport of patterns as a
Wilf-equivalence between subsets of Cayley permutations. We also highlight a
connection with primitive ascent sequences.

Combinatorics