We generalize a map by S. Mason regarding two combinatorial models for key polynomials, in a way that accounts for the major index. Furthermore we define a similar variant of this map, that regards alternative models for the modified Macdonald polynomials at t=0, and thus partially answers a question by J. Haglund. These maps together imply a certain uniqueness property regarding inversion–and coinversion-free fillings. These uniqueness properties allow us to generalize the notion of charge to a non-symmetric setting, thus answering a question by A. Lascoux and the analogous question in the symmetric setting proves a conjecture by K. Nelson.
@article{10_37236_6893,
author = {Per Alexandersson and Mehtaab Sawhney},
title = {A major-index preserving map on fillings},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {4},
doi = {10.37236/6893},
zbl = {1372.05007},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6893/}
}
TY - JOUR
AU - Per Alexandersson
AU - Mehtaab Sawhney
TI - A major-index preserving map on fillings
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/6893/
DO - 10.37236/6893
ID - 10_37236_6893
ER -
%0 Journal Article
%A Per Alexandersson
%A Mehtaab Sawhney
%T A major-index preserving map on fillings
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/6893/
%R 10.37236/6893
%F 10_37236_6893
Per Alexandersson; Mehtaab Sawhney. A major-index preserving map on fillings. The electronic journal of combinatorics, Tome 24 (2017) no. 4. doi: 10.37236/6893
