相关论文: Ideals of Quasi-Symmetric Functions and Super-Cova…

Let the symmetric group $\mathfrak{S}_n$ act on the polynomial ring $\mathbb{Q}[\mathbf{x}_n] = \mathbb{Q}[x_1, \dots, x_n]$ by variable permutation. The coinvariant algebra is the graded $\mathfrak{S}_n$-module $R_n :=…

Let $M$ and $N$ be fixed non-negative integer numbers and let $\pi_N$ be a polynomial of degree $N$. Suppose that $(P_n)_{n\geq0}$ and $(Q_n)_{n\geq0}$ are two orthogonal polynomial sequences such that %their derivatives of orders $k$ and…

A minor is principal means it is defined by the same row and column indices. Let $X$ be a square generic matrix, $K[X]$ the polynomial ring in entries of $X$, over an algebraically closed field, $K$. For fixed $t\leq n$, let $\mathfrak P_t$…

In this paper a new class of radial basis functions based on hyperbolic trigonometric functions will be introduced and studied. We focus on the properties of their generalised Fourier transforms with asymptotics. Therefore we will compute…

We define a family of ideals $I_h$ in the polynomial ring $\mathbb{Z}[x_1,...,x_n]$ that are parametrized by Hessenberg functions $h$ (equivalently Dyck paths or ample partitions). The ideals $I_h$ generalize algebraically a family of…

Let $q$ be a positive integer. In our recent paper, we proved that the cardinality of the complement of an integral arrangement, after the modulo $q$ reduction, is a quasi-polynomial of $q$, which we call the characteristic…

Let $\Omega$ be the {\em superspace ring} of polynomial-valued differential forms on affine $n$-space. The natural action of the symmetric group $\mathfrak{S}_n$ on $n$-space induces an action of $\mathfrak{S}_n$ on $\Omega$. The {\em…

Let K be a field and let A be the polynomial ring in n variables with coefficients in the field K We study the universal squarefree lexsegment ideals in A. We put our attention on their combinatorics computing some invariants. Moreover we…

The structure of Poisson polynomial algebras of the type obtained as semiclassical limits of quantized coordinate rings is investigated. Sufficient conditions for a rational Poisson action of a torus on such an algebra to leave only…

Let $\{P_n \}_{n\ge0}$ be a sequence of monic orthogonal polynomials with respect to a quasi--definite linear functional $u$ and $\{Q_n \}_{n\ge0}$ a sequence of polynomials defined by $$Q_n(x)=P_n(x)+s_n P_{n-1}(x)+t_n P_{n-2}(x),\quad…

Let $k$ be a field and $x,y$ indeterminates over $k$. Let $R=k[x^a,x^{p_1}y^{s_1},\ldots,x^{p_t}y^{s_t},y^b] \subseteq k[x,y]$. We calculate the Hilbert polynomial of $(x^a,y^b)$. The multiplicity of this ideal provides part of a criterion…

Let K be an infinite field and let R be a K-algebra endowed with a homogeneous polynomial norm N of degree n. If N satisfies a formal analogue of the Cayley-Hamilton Theorem the we will show that R is a quotient of the ring of the…

Let R be a commutative ring and let n,m be two positive integers. The symmetric group on n letters acts diagonally on the ring of polynomials in nxm variables with coefficients in R. The subrings of invariants for this action is called the…

A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient space. Cocycles form a subring of the ring of cochains,…

Let I be a conjugation-invariant ideal in the complex polynomial ring with variables z_1,...,z_n and their conjugates. The ideal I has the Quillen property if every real valued, strictly positive polynomial on the real zero set of I in C^n…

We introduce the $q,t$-Catalan measures, a sequence of piece-wise polynomial measures on $\mathbb{R}^2$. These measures are defined in terms of suitable area, dinv, and bounce statistics on continuous families of paths in the plane, and…

In the context of the ring Q[x,y], of polynomials in 2n variables x=x1,...,x_n and y=y1,...,yn, we introduce the notion of diagonally quasi-symmetric polynomials. These, also called "diagonal Temperley-Lieb invariants", make possible the…

Let $S = K[x_1, \ldots, x_n]$ denote the polynomial ring in $n$ variables over a field $K$ with each $\deg x_i = 1$ and $I \subset S$ a homogeneous ideal of $S$ with $\dim S/I = d$. The Hilbert series of $S/I$ is of the form…

Let $k \leq n$ be nonnegative integers and let $\lambda$ be a partition of $k$. S. Griffin recently introduced a quotient $R_{n,\lambda}$ of the polynomial ring $\mathbb{Q}[x_1, \dots, x_n]$ in $n$ variables which simultaneously generalizes…

Let $n$ be any natural number. Let $K$ be any $n$-dimensional knot in $S^{n+2}$. We define a supersymmetric quantum system for $K$ with the following properties. We firstly construct a set of functional spaces (spaces of fermionic \{resp.…