The University of Michigan Combinatorics Seminar
The coefficients in the polynomial
[an choose k]q
may be found explicitly.
There is another interpretation of these coefficients. For
example, the constant term is the number of double cosets
Cn \ San / (Sk
A multiset and Schur function
version is also given. A positive polynomial q-version
is conjectured which agrees with a known result
on double cosets for GLn(q) and the Singer cycle.