Signed Excedance Enumeration in the Hyperoctahedral group
Keywords: Signed excedance, permutation group, hyperoctahedral group
AbstractSeveral signed excedance-like statistics have nice formulae or generating functions when summed over the symmetric group and over its subset of derangements. We give counterparts of some of these results when we sum over the hyperoctahedral group and its subset of derangements. Our results motivate us to define and derive attractive bivariate formulae which generalise some of these results for the symmetric group.