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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 ...
Artículo
Los números de (Euler)-Catalan
(Asociación Matemática Venezolana, 2003)
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 ...
Artículo
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 ...
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
Invariants and coinvariants of the symmetric group in noncommuting variables
(University of Toronto Press, 2008)
We introduce a natural Hopf algebra structure on the space of noncommutative symmetric functions. The bases for this algebra are indexed by set partitions. We show that there exists a natural inclusion of the Hopf algebra ...
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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
Sumando la derivada de la serie geométrica
(Asociación Matemática Venezolana, 2003)
Artículo
Resolutions of De Concini-Procesi ideals of hooks
(Taylor & Francis, 2007)
We find a minimal generating set for the defining ideal of the schematic intersection of the set of diagonal matrices with the closure of the conjugacy class of a nilpotent matrix indexed by a hook partition. The structure ...