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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 ...
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Artículo
The defining ideals of conjugacy classes of nilpotent matrices and a conjecture of Weyman
(Oxford University Press, 2008)
Tanisaki introduced generating sets for the defining ideals of the schematic intersections of the closure of conjugacy classes of nilpotent matrices with the set of diagonal matrices. These ideals are naturally labeled by ...
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Combinatorics on a family of reduced Kronecker coefficients
(Académie des Sciences, 2015-08-28)
The reduced Kronecker coefficients are particular instances of Kronecker coefficients, that nevertheless contain enough information to compute all Kronecker coefficients from them. In this note, we compute the generating ...
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Los números de (Euler)-Catalan
(Asociación Matemática Venezolana, 2003)
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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 ...
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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 ...
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Grothendieck bialgebras, Partition lattices, and symmetric functions in noncommutative variables
(American Mathematical Society, 2006)
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism ...
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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 ...
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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 ...