1Otto-von-Guericke University, Magdeburg 2Max Planck Institut for Mathematics in the Sciences, Leipzig, Germany and Mathematical Institute of the Polish Academy of Sciences, Warsaw, Poland
The electronic journal of combinatorics, Tome 25 (2018) no. 1
Motivated by questions of Mulmuley and Stanley we investigate quasi-polynomials arising in formulas for plethysm. We demonstrate, on the examples of $S^3(S^k)$ and $S^k(S^3)$, that these need not be counting functions of inhomogeneous polytopes of dimension equal to the degree of the quasi-polynomial. It follows that these functions are not, in general, counting functions of lattice points in any scaled convex bodies, even when restricted to single rays. Our results also apply to special rectangular Kronecker coefficients.
1
Otto-von-Guericke University, Magdeburg
2
Max Planck Institut for Mathematics in the Sciences, Leipzig, Germany
and
Mathematical Institute of the Polish Academy of Sciences, Warsaw, Poland
@article{10_37236_6597,
author = {Thomas Kahle and Mateusz Micha{\l}ek},
title = {Obstructions to combinatorial formulas for plethysm},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/6597},
zbl = {1454.05124},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6597/}
}
TY - JOUR
AU - Thomas Kahle
AU - Mateusz Michałek
TI - Obstructions to combinatorial formulas for plethysm
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6597/
DO - 10.37236/6597
ID - 10_37236_6597
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%A Thomas Kahle
%A Mateusz Michałek
%T Obstructions to combinatorial formulas for plethysm
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6597/
%R 10.37236/6597
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Thomas Kahle; Mateusz Michałek. Obstructions to combinatorial formulas for plethysm. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/6597
