Enumerating Excedances with Linear Characters in Classical Weyl Groups
نویسنده
چکیده
Several signed excedance-type statistics have nice formulae when summed over the symmetric group and over the hyperoctahedral group. Motivated by these, we consider sums of the form fχ,n(q) = ∑ w∈W χ(w)q exc(w) where W is a classical Weyl group of rank n, χ is a non-trivial one-dimensional character of W , and exc(w) is the excedance statistic of w. We give formulae for these sums in a more general multivariate setting. We sharpen existing results for types A and B and give new results for classical Weyl groups of type B and type D.
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تاریخ انتشار 2016