  A Mahonian d-function is a Mahonian statistic that can be expressed as a
linear combination of vincular pattern statistics of length at most d. Babson
and Steingrimsson classified all Mahonian 3-functions up to trivial bijections
and identified many of them with well-known Mahonian statistics in the
literature. We prove a host of Mahonian 3-function equidistributions over
pattern avoiding sets of permutations. Tools used include block decomposition,
Dyck paths and generating functions.
