  It is well-known that the representation theory of the finite group of
unipotent upper-triangular matrices $U_n$ over a finite field is a wild
problem. By instead considering approximately irreducible representations
(supercharacters), one obtains a rich combinatorial theory analogous to that of
the symmetric group, where we replace partition combinatorics with
set-partitions. This paper studies Diaconis--Isaacs' concept of superinduction
in pattern groups. While superinduction shares many desirable properties with
usual induction, it no longer takes characters to characters. We begin by
finding sufficient conditions guaranteeing that super-induction is in fact
induction. It turns out for natural embedding of $U_m$ in $U_n$,
super-induction is induction. We conclude with an explicit combinatorial
algorithm for computing this induction analogous to the Pieri-formulas for the
symmetric group.
