Related papers: A Whitney polynomial for hypermaps

This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…

The paper introduces a method of partial fractions with matrix coefficients and its applications to finding chains of generalized eigenvectors, to evaluation of matrix exponentials, and to solution of linear systems of ordinary differential…

Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying p_S(x+y)=\sum_{T\uplus U=S}p_T(x)p_U(y). Using umbral calculus, we give a formula for the expansion of such a set map in terms of any…

We assign a new polynomial to any checkerboard-colorable 4-valent virtual graph in terms of its Euler circuit expansion. This provides a new combinatorial formulation of the Kauffman-Jones polynomial for checkerboard-colorable virtual…

A generalization of the classical Leibniz rule for the covariant derivative on a vector bundle is obtained.

We establish closed-form expansions for the universal edge elimination polynomial of paths and cycles and their generating functions. This includes closed-form expansions for the bivariate matching polynomial, the bivariate chromatic…

We extend the polynomial approach to hook length formula proposed in a recent joint paper with K\'arolyi, Nagy and Volkov to several other problems of the same type, including number of paths formula in the Young graph of strict partitions.

In this paper we propose a graph superalgebra which is the supersymmetric analogue of Leavitt path algebras. We find a basis for these superalgebras and characterize when they have polynomial growth.

We suggest a reduction of the combinatorial problem of hypergraph partitioning to a continuous optimization problem.

We propose an algorithm for solving of the graph isomorphism problem. Also, we introduce the new class of graphs for which the graph isomorphism problem can be solved polynomially using the algorithm.

We define generalized bivariate polynomials, from which upon specification of initial conditions the bivariate Fibonacci and Lucas polynomials are obtained. Using essentially a matrix approach we derive identities and inequalities that in…

In this paper, we prove a generalization of the Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety over a number field. Our result improves and generalizes the previous…

We introduce a theory of finite polynomial cohomology with coefficients in this paper. We prove several basic properties and introduce an Abel-Jacobi map with coefficients. As applications, we use such a cohomology theory to study…

This note will describe an effective procedure for constructing critically finite real polynomial maps with specified combinatorics.

We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…

We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral…

This paper considers a hyperplane arrangement constructed with a subset of a set of all simple paths in a graph. A connection of the constructed arrangement to the maximum matching problem is established. Moreover, the problem of finding…

We generalise the finite biquandle colouring invariant to a polynomial invariant based on labelling a knot diagram with a finite birack that reduces to the biquandle colouring invariant in that case. The polynomial is an invariant of a…

Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…

In this paper, we introduce a new concept namely degree polynomial for vertices of a simple graph. This notion leads to a concept namely degree polynomial sequence which is stronger than the concept of degree sequence. After obtaining the…