Séminaire Lotharingien de Combinatoire, B74c (2016), 15 pp.

Sivaramakrishnan Sivasubramanian

Enumerating Excedances With Linear Characters In Classical Weyl Groups

Abstract. 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 f\chi,n(q) = \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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