Results 21 to 30 of about 4,223,867 (200)
Journal of Algebra, 2023 Polynomial identities play a crucial role in algebraic structures, and the study of Hilbert series has been important in understanding the properties of algebras. While the Hilbert-Serre theorem states that the Hilbert series of a finitely generated commutative algebra is rational, this is not true for non-commutative algebras.
A.Ya. Belov, L. Centrone, S. Malev
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Hilbert series of residual intersections [PDF]
Compositio Mathematica, 2015 We give explicit formulas for the Hilbert series of residual intersections of a scheme in terms of the Hilbert series of its conormal modules. In a previous paper, we proved that such formulas should exist. We give applications to the number of equations defining projective varieties and to the dimension of secant varieties of surfaces and three-folds.
Chardin, Marc +2 more
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The Hilbert series of adjoint SQCD [PDF]
Nuclear Physics B, 2010 53 pages, 1 figure and 2 tables.
Hanany, Amihay +2 more
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Special Cases of the Parking Functions Conjecture and Upper-Triangular Matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We examine the $q=1$ and $t=0$ special cases of the parking functions conjecture. The parking functions conjecture states that the Hilbert series for the space of diagonal harmonics is equal to the bivariate generating function of $area$ and $dinv$ over ...
Paul Levande
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EFT asymptotics: the growth of operator degeneracy
SciPost Physics, 2021 We establish formulae for the asymptotic growth (with respect to the scaling dimension) of the number of operators in effective field theory, or equivalently the number of $S$-matrix elements, in arbitrary spacetime dimensions and with generic field ...
Tom Melia, Sridip Pal
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A Multiparameter Hardy–Hilbert-Type Inequality Containing Partial Sums as the Terms of Series
Journal of Mathematics, 2021 In this study, a multiparameter Hardy–Hilbert-type inequality for double series is established, which contains partial sums as the terms of one of the series.
Jianquan Liao, Shanhe Wu, Bicheng Yang
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The Hilbert series and a-invariant of circle invariants [PDF]
Journal of Pure and Applied Algebra, 2019 Let $V$ be a finite-dimensional representation of the complex circle $\mathbb{C}^\times$ determined by a weight vector $\mathbf{a}\in\mathbb{Z}^n$. We study the Hilbert series $\operatorname{Hilb}_{\mathbf{a}}(t)$ of the graded algebra $\mathbb{C}[V]^{\mathbb{C}_{\mathbf{a}}^\times}$ of polynomial $\mathbb{C}^\times$-invariants in terms of the weight ...
Cowie, L. Emily +3 more
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Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces [PDF]
, 2011 The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces
Hernández-Medina, Miguel A. +7 more
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Hilbert series of simple thin polyominoes [PDF]
Journal of Algebraic Combinatorics, 2021 Let P be a simple thin polyomino, roughly speaking a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert series $h(t)/(1-t)^d$ of K[P] by proving that $h(t)$ is the rook polynomial of P. As an application, we characterize the Gorenstein simple thin polyominoes.
Rinaldo G., Romeo F.
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Standard fillings to parking functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 The Hilbert series of the Garsia-Haiman module can be written as a generating function of standard fillings of Ferrers diagrams. It is conjectured by Haglund and Loehr that the Hilbert series of the diagonal harmonics can be written as a generating ...
Elizabeth Niese
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