Related papers: On Hall-Littlewood polynomials
We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree.
This is a straightforward introduction to the properties of polynomials in many variables that do not vanish in the open upper half plane. Such polynomials generalize many of the well-known properties of polynomials with all real roots.
Computations in the cohomology of finite groups.
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
The note complements topological aspects of the theory of chiral algebras.
In this paper, we survey results regarding the interlace polynomial of a graph, connections to such graph polynomials as the Martin and Tutte polynomials, and generalizations to the realms of isotropic systems and delta-matroids.
The purpose of this note is to extend in a simple and unified way some results on orthogonal polynomials with respect to the weight function $$\frac{|T_m(x)|^p}{\sqrt{1-x^2}}\;,\quad-1<x<1\;,$$ where $T_m$ is the Chebyshev polynomial of the…
This is a reference volume on polyfold and Fredholm theory.
In a recent paper Konvalinka and Lauve proved several skew Pieri rules for Hall-Littlewood polynomials. In this note we show that q-analogues of these rules are encoded in a q-binomial theorem for Macdonald polynomials due to Lascoux and…
The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical…
We show that the Littlewood-Richardson coefficients are values at 1 of certain parabolic Kazhdan-Lusztig polynomials for affine symmetric groups. These q-analogues of Littlewood-Richardson multiplicities coincide with those previously…
The analysis of solutions to algebraic equations is further simplified. A couple of functions and their analytic continuation or root findings are required.
Binet formulae for three versions of third-order Pell polynomials are derived.
In the paper, some lower bounds for polygamma functions are refined.
We consider multilinear Littlewood polynomials, polynomials in $n$ variables in which a specified set of monomials $U$ have $\pm 1$ coefficients, and all other coefficients are $0$. We provide upper and lower bounds (which are close for $U$…
Article explicitly expresses Subgraph Isomorphism by a polynomial size asymmetric linear system.
We build a variant of Collatz Conjecture for polynomials over $\mathbb{F}_2$ and we prove that it is solved. By the way, we give several examples.
I settle a conjecture of Andrews related to the Alladi-Schur polynomials. In addition, I give further relations and implications to two families of polynomials related to the Alladi-Schur polynomials.
We discuss some aspects of the theory of subelliptic estimates.
We prove that a random bivariate polynomial with plus minus 1 coefficients is irreducible with high probability.