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Artículo
Los números de (Euler)-Catalan
(Asociación Matemática Venezolana, 2003)
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
A combinatorial overview of the Hopf algebra of MacMahon symmetric functions
(Springer, 2002-11)
A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. In this article, we give a combinatorial overview of the Hopf algebra ...
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
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
MacMahon symmetric functions, the partition lattice, and young subgroups
(Elsevier, 2001-11)
A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. In this article, we show that the MacMahon symmetric functions are ...
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
Vector partition functions and Kronecker coefficients
(IOP Science, 2021-04-01)
The Kronecker coefficients are the structure constants for the restriction of irreducible representations of the general linear group GL(nm) into irreducibles for the subgroup GL(n) × GL(m). In this work we study the ...
Artículo
All linear symmetries of the SU(3) tensor multiplicities
(IOP Science, 2023-12-07)
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
Combinatorics on a family of reduced Kronecker coefficients
(Elsevier, 2015-10)
The reduced Kronecker coefficients are particular instances of Kronecker coefficients that contain enough information to recover them. In this notes we compute the generating function of a family of reduced Kronecker ...