Title: Mahonian STAT on rearrangement class of words,
Abstract: In 2000, Babson and Steingrímsson generalized the notion of permutation
patterns to the so-called vincular patterns, and they showed that many Mahonian
statistics can be expressed as sums of vincular pattern occurrence statistics.
STAT is one of such Mahonian statistics discoverd by them. In 2016, Kitaev and
the third author introduced a words analogue of STAT and proved a joint
equidistribution result involving two sextuple statistics on the whole set of
words with fixed length and alphabet. Moreover, their computer experiments
hinted at a finer involution on $R(w)$, the rearrangement class of a given word
$w$. We construct such an involution in this paper, which yields a comparable
joint equidistribution between two sextuple statistics over $R(w)$. Our
involution builds on Burstein's involution and Foata-Schützenberger's
involution that utilizes the celebrated RSK algorithm.