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Artículo
Commutation and normal ordering for operators on symmetric functions
(2019)
We study the commutation relations and normal ordering between families of operators on symmetric functions. These operators can be naturally defined by the operations of multiplication, Kronecker product, and their ...
Artículo
Artículo
On the Sn-module structure of the noncommutative harmonics
(Elsevier, 2008-08)
Using the a noncommutative version of Chevalley’s theorem due to Bergeron, Reutenauer, Rosas, and Zabrocki we compute the graded Frobenius series for their two sets of noncommutative harmonics with respect to the left ...
Artículo
Milne's volume function and vector symmetric polynomials
(Elsevier, 2009-05)
The number of real roots of a system of polynomial equations fitting inside a given box can be counted using a vector symmetric polynomial introduced by P. Milne, the volume function. We provide the expansion of Milne’s ...
Ponencia
Invariance properties for coefficients of symmetric functions
(2016)
We show that several of the main structural constants for symmetric functions (Littlewood-Richardson coefficients, Kronecker coefficients, plethysm coefficients, and the Kostka-Foulkes polynomials) share invariance properties ...
Artículo
Reduced Kronecker coefficients and counter-examples to Mulmuley's strong saturation conjecture SH
(Springer, 2009-12)
We provide counter–examples to Mulmuley’s strong saturation conjecture (strong SH) for the Kronecker coefficients. This conjecture was proposed in the setting of Geometric Complexity Theory to show that deciding whether ...
Artículo
All linear symmetries of the SU(3) tensor multiplicities
(IOP Science, 2024)
The SU(3) tensor multiplicities are piecewise polynomial of degree 1 in their labels. The pieces are the chambers of a complex of cones. We describe in detail this chamber complex and determine the group of all linear ...
Artículo
The stability of the Kronecker products of Schur functions
(Elsevier, 2011-04-01)
In the late 1930’s Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n sufficiently large, the values of the Kronecker coefficients appearing in the product ...
Artículo
Rectangular symmetries for coefficients of symmetric functions
(American Mathematical Society, 2015)
We show that some of the main structural constants for symmetric functions (Littlewood-Richardson coefficients, Kronecker coefficients, plethysm coefficients, and the Kostka–Foulkes polynomials) share symmetries related ...
Artículo
Rectangular symmetries for coe cients of symmetric functions
(The Electronic Journal of Combinatorics, 2015-07-31)
We show that some of the main structural constants for symmetric functions (Littlewood-Richardson coe cients, Kronecker coe cients, plethysm coe cients, and the Kostka{Foulkes polynomials) share symmetries related to the ...