Abstract
We show that several of the main structural constants for symmetric functions (Littlewood-Richardsoncoefficients, Kronecker coefficients, plethysm coefficients, and the Kostka–Foulkes polynomials) share invarianceproperties related to the operations of taking complements with respect to rectangles and adding rectangles. Nous montrons que plusieurs des principales constantes de structure de la théorie des fonctions symétriques(les coefficients de Littlewood–Richardson, les coefficients de Kronecker, les coefficients du pléthysme, et les polynômesde Kostka–Foulkes) ont en commun des symétries décrites par des opérations de complémentation dans des rectangleset d’ajout de rectangles pour les partitions qui les étiquettent.
Highlights
This paper investigates some invariance properties of four of the main families of coefficients in the theory of symmetric functions: the Kostka numbers, the Littlewood-Richardson, the Kronecker, and the plethysm coefficients
The presence of invariance relations often leads to a better understanding of the objects they enumerate, to simplifications in the number of cases in proofs, and in some cases, can be used to simplify computations
In this paper we present a unified approach that shows some invariance relations for all these families of coefficients
Summary
This paper investigates some invariance properties of four of the main families of coefficients in the theory of symmetric functions: the Kostka numbers (and their deformations, the Kostka–Foulkes polynomials), the Littlewood-Richardson, the Kronecker, and the plethysm coefficients. These coefficients have applications to many different fields of mathematics such as representation theory, invariant theory and algebraic geometry, as well as physics and computer science. In this paper we present a unified approach that shows some invariance relations for all these families of coefficients These relations involve two operations on partitions: (i) taking complements in rectangles, or (ii) adding “tall” rectangles.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
