Hikita polynomials are the combinatorial side of the rational shuffle theorem. Building upon a recent formula for $(m,3)$-Catalan polynomials, we prove a formula for $(m,3)$-Hikita polynomials in terms of Catalan polynomials. This formula shows a surprising relation among coefficients of Hikita polynomials and implies deeper recursive relations and proves the $q,t$-symmetry of $(m,3)$-Hikita polynomials.
@article{10_37236_6680,
author = {Ryan Kaliszewski and Debdut Karmakar},
title = {A rational {Catalan} formula for {\((m,3)\)-Hikita} polynomials},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/6680},
zbl = {1380.05193},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6680/}
}
TY - JOUR
AU - Ryan Kaliszewski
AU - Debdut Karmakar
TI - A rational Catalan formula for \((m,3)\)-Hikita polynomials
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6680/
DO - 10.37236/6680
ID - 10_37236_6680
ER -
%0 Journal Article
%A Ryan Kaliszewski
%A Debdut Karmakar
%T A rational Catalan formula for \((m,3)\)-Hikita polynomials
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6680/
%R 10.37236/6680
%F 10_37236_6680
Ryan Kaliszewski; Debdut Karmakar. A rational Catalan formula for \((m,3)\)-Hikita polynomials. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/6680
