## Double cosets and sieved q-binomial coefficients

### Denis Stanton, U. Minnesota

Abstract: The coefficients in a q-binomial coefficient mod (q^n-1) are
shown to be
equal to the number of double cosets C_n\S_n/S_k \times S_{n-k}
whose size is certain multiple. This extends an observation of Chapoton.
The result is generalized to finite Coxeter groups. q-analogues are
conjectured
which generalize results of Andrew and Haiman.
A related Schur function result is given.