Related papers: Multisymmetric polynomials in dimension three
Several relations and bounds for the dimension of principal ideals in group algebras are determined by analyzing minimal polynomials of regular representations. These results are used in the two last sections. First, in the context of…
A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,...,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of…
We present a class of homogeneous ideals which are generated by monomials and binomials of degree two and are set-theoretic complete intersections. This class includes certain reducible varieties of minimal degree and, in particular, the…
The set $S(n)$ of all elementary symmetric polynomials in $n$ variables is a minimal generating set for the algebra of symmetric polynomials in $n$ variables, but over a finite field ${\mathbb F}_q$ the set $S(n)$ is not a minimal…
We characterize monomial ideals which are intersections of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.
Let A be a finite dimensional symmetric cllular algebras. We construct a nilpotent ideal in A. The ideal connects the radicals of cell modules with the radical of the algebra. It also reveals some information on the dimensions of simple…
We propose a formal resource-theoretic approach to quantify the degree of polarization of two and three-dimensional random electromagnetic fields. This endows the space of spectral polarization matrices with the orders induced by…
We introduce the class of principal symmetric ideals, which are ideals generated by the orbit of a single polynomial under the action of the symmetric group. Fixing the degree of the generating polynomial, this class of ideals is…
A zero-dimensional polynomial ideal may have a lot of complex zeros. But sometimes, only some of them are needed. In this paper, for a zero-dimensional ideal $I$, we study its complex zeros that locate in another variety $\textbf{V}(J)$…
We give two examples where symmetric polynomials play an important role in physics: First, the partition functions of ideal quantum gases are closely related to certain symmetric polynomials, and a part of the corresponding theory has a…
Motivated by a question in Schubert calculus, we study the interplay of quasisymmetric polynomials with the divided symmetrization operator, which was introduced by Postnikov in the context of volume polynomials of permutahedra. Divided…
Given vertex valencies admissible for a self-dual polyhedral graph, we describe an algorithm to explicitly construct such a polyhedron. Inputting in the algorithm permutations of the degree sequence can give rise to non-isomorphic graphs.…
In this paper we introduce and investigate a one-parameter family of polynomials. They are semisymmetric, i.e. symmetric in the variables with odd and even index separately. In fact, the family forms a basis of the space of semisymmetric…
It is well-known that the Pl\"ucker relations generate the ideal of relations of the maximal minors of a generic matrix. In this paper we discuss the relations between minors of a (non-maximal) fixed size. We will exhibit minimal relations…
It is shown that a trivial version of polarization is sufficient to produce separating systems of polynomial invariants: if two points in the direct sum of the $G$--modules $W$ and $m$ copies of $V$ can be separated by polynomial…
Any multilinear non-central polynomial $p$ (in several noncommuting variables) takes on values of degree $n$ in the matrix algebra $M_n(F)$ over an infinite field $F$. The polynomial $p$ is called {\it $\nu$-central} for $M_n(F)$ if $p^\nu$…
Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is generated by three monomials of degrees $d$. If the Stanley depth of $I/J$ is…
We bound the tensor ranks of elementary symmetric polynomials, and we give explicit decompositions into powers of linear forms. The bound is attained when the degree is odd.
A new polynomial sieve is presented and used to show that almost all integers have at most one representation as a sum of two values of a given polynomial of degree at least 3.
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…