Related papers: Index Polynomials for Virtual Tangles

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

We consider involutory virtual biracks with good involutions, also known as symmetric involutory virtual biracks. Any good involution on an involutory virtual birack defines an enhancement of the counting invariant. We provide examples…

We define an indicial polynomial of a $D$-module along an arbitrary subvariety as a generalization of both the classical indicial polynomial for a single linear differential equation and the Bernstein-Sato polynomial of a variety defined by…

Geometric interpretations of some virtual knot invariants are given in terms of invariants of links in $\mathbb{S}^3$. Alexander polynomials of almost classical knots are shown to be specializations of the multi-variable Alexander…

This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.

Vassiliev invariants up to order six for arbitrary torus knots $\{ n , m \}$, with $n$ and $m$ coprime integers, are computed. These invariants are polynomials in $n$ and $m$ whose degree coincide with their order. Furthermore, they turn…

In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…

We compute the involutive knot invariants for pretzel knots of the form P(-2,m,n) for m and n odd and greater than or equal to 3.

We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.

Some integral properties of Jack polynomials, hypergeometric functions and invariant polynomials are studied for real normed division algebras.

We derive inclusion regions for the eigenvalues of matrix polynomials expressed in a general polynomial basis, which can lead to significantly better results than traditional bounds. We present several applications to engineering problems.

We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our…

As a generalization of the classical knots, knotoids deal with the open ended knot diagrams in a surface. In recent years, many polynomial invariants for knotoids have appeared, such as the bracket polynomial, the index polynomial and the…

The Eynard-Orantin invariants of a plane curve are multilinear differentials on the curve. For a particular class of genus zero plane curves these invariants can be equivalently expressed in terms of simpler expressions given by polynomials…

It is interesting to know, how far we can generalize the notion of a group-valued cocycle keeping the property to determine a bundle. We find a generalization for pairs of cocycles and show how these generalized pairs of cocycles can still…

We characterize atypical values at infinity of a real polynomial function of three variables by a certain sum of indices of the gradient vector field of the function restricted to a sphere with a sufficiently large radius. This is an…

In this note, we introduce and investigate the Hermite-based Tangent numbers and polynomials, Hermite-based modifieed degenerate- Tangent polynomials, poly-Tangent polynomials. We give some identities and relations for these polynomials.

In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.

For an algebraically closed field $K$ of characteristic zero and a non-singular matrix $A\in \mbox{GL}_n(K)$, a semi-invariant polynomial of $A$ is defined to be a polynomial $p(x)=p(x_1,\dots,x_n)$ with coefficients in $K$ such that…