Let p 1 p n 0, and p = detkx p j i k n i;j=1. Let Mp be the linear span of the partial derivatives of p. Then Mp is a graded Sn-module. We prove that it is the direct sum of graded left regular representations of Sn. Speciically, set j = p j , n , j, and let t be the Hilbert polynomial of the span of all skew Schur functions s = as varies in. Then the graded Frobenius characteristic of Mp is t ...

where the subscript j on the right of a graded module denotes, throughout the paper, the degree j component of that module. There are two monomial ideals canonically attached to I: the generic initial ideal Gin(I) with respect to the revlex order and the lex-segment ideal Lex(I). They play a fundamental role in the investigation of many algebraic, homological, combinatorial and geometric proper...

BACKGROUND Signaling through mitogen-activated protein kinase (MAPK) cascade pathways can show various input-output behaviors, including either switch-like or graded responses to increasing levels of stimulus. Prior studies suggest that switch-like behavior is promoted by positive feedback loops and nonprocessive phosphorylation reactions, but it is unclear whether graded signaling is a default...

We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W = G(m, p, n), and give supporting evidence that this space seems to always be isomorphic, as a graded W -module, to the undeformed version. Résumé. Nous introduisons une déformation de l’espace des polynômes harmoniques (multi-diagonaux) pour tout groupe de réfle...

We provide a new algebraic description of the structure on the set of all unstable cohomology operations for a suitable generalised cohomology theory, E(−). Our description is as a graded and completed version of a Tall-Wraith monoid. The E-cohomology of a space X is a module for this Tall-Wraith monoid. We also show that the corresponding Hopf ring of unstable co-operations is a module for the...

EÎ'(X, A) = Ê\T, H\X, A)) where H denotes the Tate cohomology ofir [l, Chapter 12 ] and H'(X, A) is the jth Cech cohomology group of (X, A) with arbitrary coefficients and with w action induced by that on X. The term Ew is the graded module associated with a certain filtered module J*(XyA). This sequence is natural with respect to ir-equivariant maps of (X, A). If w acts trivially on X, the seq...

In this paper, considering the difference between the finiteness dimension and cohomological dimension for a finitely generated module, we investigate the asymptotic behavior of grades of components of graded local cohomology modules with respect to irrelevant ideal; as long as we study some artinian and tameness property of such modules.

We give a Hodge-theoretic interpretation of the multi-plier ideal of an effective divisor on a smooth complex variety. More precisely, we show that the associated graded coherent sheaf with respect to the jumping-number filtration can be recovered from the smallest piece of M. Saito's Hodge filtration of the D-module of vanishing cycles.