Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple of identities showing that skew Jack symmetric functions are semi-invariant up to translation and rotation of a $\pi$ angle of the skew diagram. It follows that, in some special cases, the coefficients of the skew Jack symmetric functions with respect to the basis of the monomial symmetric functions are polynomials with nonnegative integer coefficients.
@article{10_37236_10542,
author = {Paolo Bravi and Jacopo Gandini},
title = {Some combinatorial properties of skew {Jack} symmetric functions},
journal = {The electronic journal of combinatorics},
year = {2022},
volume = {29},
number = {2},
doi = {10.37236/10542},
zbl = {1487.05268},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10542/}
}
TY - JOUR
AU - Paolo Bravi
AU - Jacopo Gandini
TI - Some combinatorial properties of skew Jack symmetric functions
JO - The electronic journal of combinatorics
PY - 2022
VL - 29
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/10542/
DO - 10.37236/10542
ID - 10_37236_10542
ER -
%0 Journal Article
%A Paolo Bravi
%A Jacopo Gandini
%T Some combinatorial properties of skew Jack symmetric functions
%J The electronic journal of combinatorics
%D 2022
%V 29
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/10542/
%R 10.37236/10542
%F 10_37236_10542
Paolo Bravi; Jacopo Gandini. Some combinatorial properties of skew Jack symmetric functions. The electronic journal of combinatorics, Tome 29 (2022) no. 2. doi: 10.37236/10542
