  The study of Mahonian statistics dated back to 1915 when MacMahon showed that
the major index and the inverse number have the same distribution on a set of
permutations with length n. Since then, many Mahonian statistics have been
discovered and much effort have been done to find the equidistribution between
two Mahonian statistics on permutations avoiding length-3 classical patterns.
In recent years, Amini and Do et al. have done extensive research with various
methods to prove the equidistributions, ranging from using generating
functions, Dyck paths, block decompositions, to bijections. In this thesis, we
will solve the conjectured equidistribution between bast and foze on Av(312)
using the bijection method, as well as refine two established results by Do et
al. with a combinatorial approach.
