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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
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
Inequalities between Littlewood–Richardson coefficients
(Elsevier, 2006-05)
We prove that a conjecture of Fomin, Fulton, Li, and Poon, associated to ordered pairs of partitions, holds for many infinite families of such pairs. We also show that the bounded height case can be reduced to checking ...