Monomial basis
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Parallel Krylov Solvers for the Polynomial Eigenvalue Problem in SLEPc Open
Polynomial eigenvalue problems are often found in scientific computing applications. When the coefficient matrices of the polynomial are large and sparse, usually only a few eigenpairs are required and projection methods are the best choic…
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Numerical Solutions of Volterra Integral Equations of the Second Kind using Lagrange interpolation via the Vandermonde matrix Open
A new method is established for solving Volterra integral equations of the second kind using Lagrange interpolation through the Vandermonde approach. The goal is to minimize the interpolation errors of the high-degree polynomials on equidi…
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On deep holes of generalized Reed-Solomon codes Open
Determining deep holes is an important topic in decoding Reed-Solomon codes.\nIn a previous paper [8], we showed that the received word $u$ is a deep hole of\nthe standard Reed-Solomon codes $[q-1, k]_q$ if its Lagrange interpolation\npoly…
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Beyond Grobner Bases: Basis Selection for Minimal Solvers Open
Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this pape…
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M4GB Open
This paper introduces a new efficient algorithm for computing Gröbner-bases named M4GB. Like Faugère's algorithm F4 it is an extension of Buchberger's algorithm that describes: how to store already computed (tail-)reduced multiples of basi…
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On pseudo symmetric monomial curves Open
We study monomial curves, toric ideals and monomial algebras associated to
\n4-generated pseudo symmetric numerical semigroups. Namely, we determine
\nindispensable binomials of these toric ideals, give a characterization for these
\nmonom…
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Truncated Normal Forms for Solving Polynomial Systems: Generalized and\n Efficient Algorithms Open
We consider the problem of finding the isolated common roots of a set of\npolynomial functions defining a zero-dimensional ideal I in a ring R of\npolynomials over C. Normal form algorithms provide an algebraic approach to\nsolve this prob…
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Minimal models for monomial algebras Open
Using combinatorics of chains going back to works of Anick, Green, Happel and Zacharia, we give, for any monomial algebra $A$, an explicit description of its minimal model. This also provides us with formulas for a canonical $A_\infty$-str…
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-PURITY VERSUS LOG CANONICITY FOR POLYNOMIALS Open
In this article, we consider the conjectured relationship between $F$ -purity and log canonicity for polynomials over $\mathbb{C}$ . In particular, we show that log canonicity corresponds to dense $F$ -pure type for all polynomials whose s…
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Border Ranks of Monomials Open
Young flattenings, introduced by Landsberg and Ottaviani, give determinantal equations for secant varieties and their non-vanishing provides lower bounds for border ranks of tensors and in particular polynomials. We study monomial-optimal …
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A Polynomial-Division-Based Algorithm for Computing Linear Recurrence Relations Open
International audience
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The Singular Support of the Ising Model Open
We prove a new quasiparticle sum expression for the character of the Ising model vertex algebra, related to the Jackson–Slater $q$-series identity of Rogers–Ramanujan type and to Nahm sums for the matrix $\left (\begin {smallmatrix}8&3\\3&…
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Standard Monomial Theory and the Work of Demazure Open
In collaboration with V. Lakshmibai and C. Musili (cf.[8], [9], [10],[12]), we have given a generalization of the classical Hodge-Young standard monomial theory (cf[4], [5]) of SL(n) to the case of an arbitrary semisimple linear algebraic …
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Hopf algebras of parking functions and decorated planar trees Open
We construct three new combinatorial Hopf algebras based on the Loday-Ronco operations on planar binary trees. The first and second algebras are defined on planar trees and labeled planar trees extending the Loday-Ronco and Malvenuto-Reute…
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Spurious Vanishing Problem in Approximate Vanishing Ideal Open
Approximate vanishing ideal is a concept from computer algebra that studies the algebraic varieties behind perturbed data points. To capture the nonlinear structure of perturbed points, the introduction of approximation to exact vanishing …
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PBW-type filtration on quantum groups of type $A_n$ Open
We will introduce an $\mathbb{N}$-filtration on the negative part of a quantum group of type $A_n$, such that the associated graded algebra is a q-commutative polynomial algebra. This filtration is given in terms of the representation theo…
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Construction of determinants for the six-vertex model with domain wall boundary conditions Open
We consider the problem of construction of determinant formulas for the partition function of the six-vertex model with domain wall boundary conditions that depend on two sets of spectral parameters. In the pioneering works of Korepin and …
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Gradient Boosts the Approximate Vanishing Ideal Open
In the last decade, the approximate vanishing ideal and its basis construction algorithms have been extensively studied in computer algebra and machine learning as a general model to reconstruct the algebraic variety on which noisy data ap…
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Monomial basis in Korenblum type spaces of analytic functions Open
[EN] It is shown that the monomials A = (z(n))(n=0)(infinity) are a Schauder basis of the Frechet spaces A(+)(-gamma), gamma >= 0, that consists of all the analytic functions f on the unit disc such that (1 - vertical bar z vertical bar)(m…
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On polynomial solutions of linear integro-differential equations Open
We develop an efficient algorithm for computing polynomial solutions of linear integro-differential equations. Considering a linear integro-differential operator written in normal form, we compute the possible degrees of its polynomial sol…
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FFLV-type monomial bases for type Open
We present a combinatorial monomial basis (or, more precisely, a family of monomial bases) in every finite-dimensional irreducible -module. These bases are in many ways similar to the FFLV bases for types and . They are also defined com…
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A Galerkin-type approach to solve systems of linear Volterra-Fredholm integro-differential equations Open
The main interest of this paper is to propose a numerical scheme in order to solve linear systems of Volterra-Fredholm integro-differential equations given with mixed conditions. The proposed method is a weighted residual scheme which uses…
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Mathematical programming formulations for piecewise polynomial functions Open
This paper studies mathematical programming formulations for solving optimization problems with piecewise polynomial (PWP) constraints. We elaborate on suitable polynomial bases as a means of efficiently representing PWPs in mathematical p…
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Standard monomials and invariant theory for arc spaces III: special linear group Open
This is the third in a series of papers on standard monomial theory and invariant theory of arc spaces. For any algebraically closed field $K$, we prove the arc space analogue of the first and second fundamental theorems of invariant theor…
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Commutative Algebra: Geometric, Homological, Combinatorial and Computational Aspects Open
A Theorem of Eakin and Sathaye and Green's Hyperplane Restriction Theorem. Liaison of Varieties of Small Dimension and Deficiency Modules. Regularity Jumps for Powers of Ideals. Integral Closure of Ideals and Annihilators of Homology. Poin…
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Gröbner-Shirshov Bases for Temperley-Lieb Algebras of Complex Reflection Groups Open
We construct a Gröbner-Shirshov basis of the Temperley-Lieb algebra T ( d , n ) of the complex reflection group G ( d , 1 , n ) , inducing the standard monomials expressed by the generators { E i } of T ( d , n ) . This result generalizes …
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Numerically Stable Polynomially Coded Computing Open
We study the numerical stability of polynomial based encoding methods, which has emerged to be a powerful class of techniques for providing straggler and fault tolerance in the area of coded computing. Our contributions are as follows: 1) …
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STRUCTURE OF ENGLISH BUSINESS MONOMIALS Open
The given article presents the analysis and description of the structure assoctiated with business monomials in the English terminology. The research carries on to the breakdown of the English business monomials that fall under three group…
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Monomial difference ideals Open
In this paper, basic properties of monomial difference ideals are studied. We prove the finitely generated property of well-mixed difference ideals generated by monomials. Furthermore, a finite prime decomposition of radical well-mixed mon…
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Multiplicities of jumping numbers Open
We study multiplicities of jumping numbers of multiplier ideals in a smooth variety of arbitrary dimension. We prove that the multiplicity function is a quasi-polynomial, hence proving that the Poincar\'e series is a rational function. We …