A Generalized Mahonian Statistic on Absorption Ring Mappings

Based on a coin-tossing scheme, a generalized Mahonian statistic is defined on absorption ring mappings and applied in obtaining combinatorial interpretations of the coefficient ofqjin the expansion of ∏ki=1 (1+q+q2+…+qmi). In the permutation case, the statistic coincides with one studied by Han that specializes many known Mahonian statistics.