We exploit the connection between dominance drawings of directed acyclic
graphs and permutations, in both directions, to provide improved bounds on the
size of universal point sets for certain types of dominance drawing and on
superpatterns for certain natural classes of permutations. In particular we
show that there exist universal point sets for dominance drawings of the Hasse
diagrams of width-two partial orders of size O(n^{3/2}), universal point sets
for dominance drawings of st-outerplanar graphs of size O(n\log n), and
universal point sets for dominance drawings of directed trees of size O(n^2).
We show that 321-avoiding permutations have superpatterns of size O(n^{3/2}),
riffle permutations (321-, 2143-, and 2413-avoiding permutations) have
superpatterns of size O(n), and the concatenations of sequences of riffles and
their inverses have superpatterns of size O(n\log n). Our analysis includes a
calculation of the leading constants in these bounds.Comment: ANALCO 2014, This version fixes an error in the leading constant of
the 321-superpattern siz