Related papers: Hilbert quasi-polynomial for order domains and app…
Hilbert order is widely applied in many areas. However, most of the algorithms are confined to low dimensional cases. In this paper, algorithms for encoding and decoding arbitrary dimensional Hilbert order are presented. Eight algorithms…
In this paper, we will study some connections between Hilbert al- gebras and binary block-codes.With these codes, we can eassy obtain orders which determine suplimentary properties on these algebras. We will try to emphasize how, using…
In this paper, firstly, some applications of Hilbert matrix in image processing and cryptology are mentioned and an algorithm related to the Hilbert view of a digital image is given. In section 2, the new matrix domains are constructed and…
The Hilbert function of a module over a positively graded algebra is of quasi-polynomial type (Hilbert--Serre). We derive an upper bound for its grade, i.e. the index from which on its coefficients are constant. As an application, we give a…
We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm…
The Hilbert function, its generating function and the Hilbert polynomial of a graded ring R have been extensively studied since the famous paper of Hilbert: Ueber die Theorie der algebraischen Formen [Hil90]. In particular, the coefficients…
We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that…
We give an algebraic characterization of half-factorial orders in algebraic number fields. This generalizes prior results for seminormal orders and for orders in quadratic number fields.
The characteristic polynomial plays an important role in study of hyperplane arrangements. There are several refinements of the characteristic polynomial. One of them is the coboundary polynomial defined by Crapo. Another refinement is the…
This paper presents algorithms and pseudocode for encoding and decoding 3D Hilbert orderings.
Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…
We prove that a Hilbert domain which is quasi-isometric to a normed vector space is actually a convex polytope.
A high-order quadrature algorithm is presented for computing integrals over curved surfaces and volumes whose geometry is implicitly defined by the level sets of (one or more) multivariate polynomials. The algorithm recasts the implicitly…
We study two polynomial counting questions in arithmetic statistics via a combination of Fourier analytic and arithmetic methods. First, we obtain new quantitative forms of Hilbert's Irreducibility Theorem for degree $n$ polynomials $f$…
Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…
This paper is devoted to studying difference indices of quasi-prime difference algebraic systems. We define the quasi dimension polynomial of a quasi-prime difference algebraic system. Based on this, we give the definition of the difference…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
We compute the Hilbert series of the space of $n=3$ variable quasi-invariant polynomials in characteristic $2$ and $3$, capturing the dimension of the homogeneous components of the space, and explicitly describe the generators in the…