Related papers: Weight recursions for any rotation symmetric Boole…

We establish a connection between the function space BMO and the theory of quasisymmetric mappings on \emph{spaces of homogeneous type} $\widetilde{X} :=(X,\rho,\mu)$. The connection is that the logarithm of the generalised Jacobian of an…

As a natural basis of the Hopf algebra of quasisymmetric functions, monomial quasisymmetric functions are formal power series defined from compositions. The same definition applies to left weak compositions, while leads to divergence for…

Let $h(B_d)$ denote the space of real-valued harmonic functions on the unit ball $B_d$ of $\mathbb{R}^d$, $d\ge 2$. Given a radial weight $w$ on $B_d$, consider the following problem: construct a finite family $\{f_1, f_2, \dots, f_J\}$ in…

In this paper we discuss the notion of reducibility for matrix weights and introduce a real vector space $\mathcal C_\mathbb{R}$ which encodes all information about the reducibility of $W$. In particular a weight $W$ reduces if and only if…

We continue the study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we show the following results: Theorem A: The multiple…

A recursion operator is an integro-differential operator which maps a generalized symmetry of a nonlinear PDE to a new symmetry. Therefore, the existence of a recursion operator guarantees that the PDE has infinitely many higher-order…

We study "canonical weight decompositions" slightly generalizing that defined by J. Wildeshaus. For an triangulated category $C$, any integer $n$, and a weight structure $w$ on $C$ a triangle $LM\to M\to RM\to LM[1]$, where $LM$ is of…

It is well known that if a finite order linear differential operator with polynomial coefficients has as eigenfunctions a sequence of orthogonal polynomials with respect to a positive measure (with support in the real line), then its order…

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…

We consider the action on $\mathbb{F}_2^n$ by cyclic permutations ($\mathbb{Z}/n\mathbb{Z}$). Two elements $x, y\in \mathbb{F}_2^n$ are in the same orbit if they are cyclic shifts of each other. Cryptographic properties of rotation…

We give and prove an optimal exact quantum query algorithm with complexity $k+1$ for computing the promise problem (i.e., symmetric and partial Boolean function) $DJ_n^k$ defined as: $DJ_n^k(x)=1$ for $|x|=n/2$, $DJ_n^k(x)=0$ for $|x|$ in…

Determining the weight distribution of a linear code is a classical and fundamental topic in coding theory that has been extensively investigated. Repeated-root cyclic codes, which form a significant subclass of error-correcting codes, have…

The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case…

The main purpose of this paper is to obtain an explicit expression of a family of matrix valued orthogonal polynomials {P_n}_n, with respect to a weight W, that are eigenfunctions of a second order differential operator D. The weight W and…

We investigate polynomial sets {P n } n$\ge$0 with generating power series of the form F (xt -- R(t)) and satisfying, for n $\ge$ 0, the (d + 1)-order recursion xP\_ n (x) = P\_{ n+1 }(x) +\sum\_{ l=0}^{d} \gamma^{l}\_{n} P\_{ n--l} (x),…

Let \bar{M}_{0,n} be the moduli space of pointed, genus 0 curves. Let L_i denote the line bundle on \bar{M}_{0,n} associated to the i-th marked point (the fiber of L_i is the cotangent space of the pointed curve at the i-th point).…

Let $f_n$ be a function assigning weight to each possible triangle whose vertices are chosen from vertices of a convex polygon $P_n$ of $n$ sides. Suppose ${\mathcal T}_n$ is a random triangulation, sampled uniformly out of all possible…

Let $\mathbb{R}=(-\infty,\infty)$, and let $Q\in C^1(\mathbb{R}): \mathbb{R}\rightarrow[0,\infty)$ be an even function. We consider the exponential weights $w(x)=e^{-Q(x)}$, $x\in \mathbb{R}$. In this paper we obtain a pointwise convergence…

In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking values in the…

Linear recursions of degree $k$ are determined by evaluating the sequence of Generalized Fibonacci Polynomials, $\{F_{k,n}(t_1,...,t_k)\}$ (isobaric reflects of the complete symmetric polynomials) at the integer vectors $(t_1,...,t_k)$. If…