相关论文: On equations defining coincident root loci

Root systems are sets with remarkable symmetries and therefore they appear in many situations in mathematics. Among others, denominator formulae of root systems are very beautiful and mysterious equations which have several meanings from a…

Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…

We identify the complexity of the classification problem for automorphisms of a given countable regularly branching tree up to conjugacy. We consider both the rooted and unrooted cases. Additionally, we calculate the complexity of the…

We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…

There are several researches on Lie algebras and Lie superalgebras graded by finite root systems. In this paper, we study Leibniz algebras graded by finite root systems and obtain some results in simply-laced cases.

We study a coderivation from a cobimodule into a coalgebra. Vector cofields are defined by the action of a codual bicomodule on a coalgebra. This action is induced by a codifferential. A construction of a codual object in the category of…

Ordered pairs of proper, non-empty real projective conics can be classified modulo rigid isotopy and ambient isotopy. We characterize the classes by equations, inequations and inequalities in the coefficients of the quadratic forms defining…

We show that a monic univariate polynomial over a field of characteristic zero, with $k$ distinct non-zero known roots, is determined by its $k$ proper leading coefficients by providing an explicit algorithm for computing the multiplicities…

We give an explicit upper bound for the number of equivalence classes of binary forms with rational integral coefficients of given degree and given discriminant, and with given splitting field. Further, we give an explicit upper bound for…

Planar coincidence site lattices and modules with N-fold symmetry are well understood in a formulation based on cyclotomic fields, in particular for the class number one case, where they appear as certain principal ideals in the…

We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…

We deal with the existing problem of filtered multiplicative bases of finite-dimensional associative algebras. For an associative algebra A over a field, we investigate when the property of having a filtered multiplicative basis is…

This is a collection of articles, written as sections, on arithmetic properties of differential equations, holomorphic foliations, Gauss-Manin connections and Hodge loci. Each section is independent from the others and it has its own…

An algorithm is proposed that solves two decision problems for pseudo-Anosov elements in the mapping class group of a surface with at least one marked fixed point. The first problem is the root problem: decide if the element is a power and…

In this paper, we study the root distribution of some univariate polynomials $W_n(z)$ satisfying a recurrence of order two with linear polynomial coefficients over positive numbers. We discover a sufficient and necessary condition for the…

We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…

This is an exposition in order to give an explicit way to understand (1) a non-topological proof for an existence of a base of an affine root system, (2) a Serre-type definition of an elliptic Lie algebra with rank =>2, and (3) the…

This paper provides insights into the role of symmetry in studying polynomial functions vanishing to high order on an algebraic variety. The varieties we study are singular loci of hyperplane arrangements in projective space, with emphasis…

This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…

At the beginning of the study of the bispectral problem, see [18], the ad-conditions played a crucial role in finding non-classical instances. The connection with the ad-conditions has reappeared in several different incarnations of the…