Séminaire Lotharingien de Combinatoire, B74c (2016), 15 pp.
Enumerating Excedances With Linear Characters In
Classical Weyl Groups
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
\sumw in W \chi(w) qexc(w) where
W is a classical Weyl group of rank n, \chi 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.
Received: July 24, 2015.
Revised: April 29, 2016.
Accepted: May 4, 2016.
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