The University of Michigan Combinatorics Seminar


Abstract 

The coefficients in the polynomial
[an choose k]_{q}
mod (q^{n}1),
may be found explicitly.
There is another interpretation of these coefficients. For
example, the constant term is the number of double cosets
C_{n} \ S_{an} / (S_{k}
x S_{ank}).
A multiset and Schur function
version is also given. A positive polynomial qversion
is conjectured which agrees with a known result
on double cosets for GL_{n}(q) and the Singer cycle.
