Given a set
of permutations,
a
-superpattern
is a permutation that contains every permutation in
as a
pattern. The study of the minimum length of a superpattern has been of interest. For
being
the set of all permutations of a given length, bounds on the minimum length have been
improved over the years, and the minimum length is conjectured to be asymptotic
with
.
Similar questions have been considered for the set of layered permutations. We
consider superpatterns with respect to packing colored permutations or multiple
copies of permutations. Some simple but interesting observations will be presented.
We also propose a few questions.
