Related papers: Hilbert Functions of Chopped Ideals
The graded Betti numbers of the minimal free resolution (and also therefore the Hilbert function) of the ideal of a fat point subscheme Z of P^2 are determined whenever Z is supported at any 6 or fewer distinct points. All results hold over…
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and…
We study the closed convex hull of various collections of Hilbert functions. Working over a standard graded polynomial ring with modules that are generated in degree zero, we describe the supporting hyperplanes and extreme rays for the…
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…
This paper is devoted to understanding the defining ideal of a Nichols algebra from the decomposition of specific elements in the group algebra of braid groups. A family of primitive elements are found and algorithms are proposed. To prove…
The problem of determining the (least) fixpoint of (higher-dimensional) functions over the non-negative reals frequently occurs when dealing with systems endowed with a quantitative semantics. We focus on the situation in which the…
The elements of a finite partial order $P$ can be identified with the maximal indecomposable two-sided ideals of its incidence algebra $\A$, and then for two such ideals, $I\prec J \iff IJ \not=0$. This offers one way to recover a poset…
We study the Hilbert series of a family of ideals J_\phi generated by powers of linear forms in k[x_1,...,x_n]. Using the results of Emsalem-Iarrobino, we formulate this as a question about fatpoints in P^{n-1}. In the three variable case…
Based on the structure theory of pairs of skew-symmetric matrices, we give a conjecture for the Hilbert series of the exterior algebra modulo the ideal generated by two generic quadratic forms. We show that the conjectured series is an…
For a graded ideal I in a graded ring, the deviation of I is defined as the difference between the minimal number of generators of I and its grade. In this article, we provide bigraded free resolutions of the symmetric algebras for specific…
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…
We study those operators on a Hilbert space that can be lifted / extended to any twisted Hilbert space. We prove that these form an ideal of operators which contains all the Schatten classes. We characterize those multiplication operators…
There are several remarks on Hilbert series of finitely presented (f. p.) associative algebras over a field and their modules. First, given an integer $D$, the set of Hilbert series of right-sided ideals with generators and relations of…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
We present a survey of past research activities and current results in constructing a mathematical framework describing the principle of local reflexivity for operator ideals and reveal further applications involving operator ideal products…
We consider inequalities where integrals are defined in the sense of Choquet with respect to Hausdorff content. We study cases where continuously differentiable functions are defined on open, connected sets with so much regularity that…
We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…
We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularly relevant when the function is assumed to belong to a…
We investigate quasisymmetric functions coming from combinatorial Hopf monoids. We show that these invariants arise naturally in Ehrhart theory, and that some of their specializations are Hilbert functions for relative simplicial complexes.…
The Hilbert scheme H^d_n of n points in A^d contains an irreducible component R^d_n which generically represents n distinct points in A^d. We show that when n is at most 8, the Hilbert scheme H^d_n is reducible if and only if n = 8 and d >=…