In [Duane, Garsia, Zabrocki 2013] the authors introduced a new dinv statistic, denoted ndinv, on the two part case of the shuffle conjecture (Haglund et al. 2005) in order to prove a compositional refinement. Though in [Hicks, Kim 2013] a non-recursive (but algorithmic) definition of ndinv has been given, this statistic still looks a bit unnatural. In this paper we "unveil the mystery" around the ndinv, by showing bijectively that the ndinv actually matches the usual dinv statistic in a special case of the generalized Delta conjecture in [Haglund, Remmel, Wilson 2018]. Moreover, we give also a non-compositional proof of the "ehh" case of the shuffle conjecture (after [Garsia, Xin, Zabrocki 2014]) by bijectively proving a relation with the two part case of the Delta conjecture.
@article{10_37236_8588,
author = {Michele D'Adderio and Alessandro Iraci},
title = {The new dinv is not so new},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/8588},
zbl = {1420.05175},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8588/}
}
TY - JOUR
AU - Michele D'Adderio
AU - Alessandro Iraci
TI - The new dinv is not so new
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8588/
DO - 10.37236/8588
ID - 10_37236_8588
ER -
%0 Journal Article
%A Michele D'Adderio
%A Alessandro Iraci
%T The new dinv is not so new
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8588/
%R 10.37236/8588
%F 10_37236_8588
Michele D'Adderio; Alessandro Iraci. The new dinv is not so new. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8588
