The University of Michigan Combinatorics Seminar
Winter 2003
March 7, 4:10-5:00, 3866 East Hall

q-binomial coefficients and cyclic groups

Dennis Stanton

University of Minnesota


The coefficients in the polynomial [an choose k]q mod (qn-1), 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 x San-k). 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.