Schubert polynomials are refined by the key polynomials of Lascoux-Schützen-berger, which in turn are refined by the fundamental slide polynomials of Assaf-Searles. In this paper we determine which fundamental slide polynomial refinements of key polynomials, indexed by strong compositions, are multiplicity free. We also give a recursive algorithm to determine all terms in the fundamental slide polynomial refinement of a key polynomial indexed by a strong composition. From here, we apply our results to begin to classify which fundamental slide polynomial refinements, indexed by weak compositions, are multiplicity free. We completely resolve the cases when the weak composition has at most two nonzero parts or the sum has at most two nonzero terms.
@article{10_37236_9858,
author = {Soojin Cho and Stephanie van Willigenburg},
title = {Slide multiplicity free key polynomials},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {1},
doi = {10.37236/9858},
zbl = {1481.05155},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9858/}
}
TY - JOUR
AU - Soojin Cho
AU - Stephanie van Willigenburg
TI - Slide multiplicity free key polynomials
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/9858/
DO - 10.37236/9858
ID - 10_37236_9858
ER -
%0 Journal Article
%A Soojin Cho
%A Stephanie van Willigenburg
%T Slide multiplicity free key polynomials
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/9858/
%R 10.37236/9858
%F 10_37236_9858
Soojin Cho; Stephanie van Willigenburg. Slide multiplicity free key polynomials. The electronic journal of combinatorics, Tome 29 (2022) no. 1. doi: 10.37236/9858
