Related papers: Laurent polynomials of planar graphs

We present a means of formulating and solving graph coloring problems with probabilistic graphical models. In contrast to the prevalent literature that uses factor graphs for this purpose, we instead approach it from a cluster graph…

The well known Wagner's theorem states that a graph is a planar graph if and only if it is $K_5$-minor-free and $K_{3,3}$-minor-free. Denote by $AT(G)$ the Alon-Tarsi number of a graph $G$. We show that for any $K_{3,3}$-minor-free graph…

We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials, and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves…

We present a common generalization of counting lattice points in rational polytopes and the enumeration of proper graph colorings, nowhere-zero flows on graphs, magic squares and graphs, antimagic squares and graphs, compositions of an…

We give a new treatment of tabular LR parsing, which is an alternative to Tomita's generalized LR algorithm. The advantage is twofold. Firstly, our treatment is conceptually more attractive because it uses simpler concepts, such as grammar…

We apply tropical geometry to study the image of a map defined by Laurent polynomials with generic coefficients. If this image is a hypersurface then our approach gives a construction of its Newton polytope.

In the article we develop Euler-Lagrange method and calculate all the roots of an arbitrary complex polynomial $P(z)$ on the base of calculation (similar to the Bernoulli-Aitken-Nikiporets methods) of the limits of ratios of Hadamard…

By using an approach of the invariant theory we obtain a new formula for the ordinary generating function of the numbers of the simple graphs with $n$ nodes.

We consider polynomial maps described by so-called "(multivariate) linearized polynomials". These polynomials are defined using a fixed prime power, say q. Linearized polynomials have no mixed terms. Considering invertible polynomial maps…

We introduce non-associative skew Laurent polynomial rings and characterize when they are simple. Thereby, we generalize results by Jordan, Voskoglou, and Nystedt and \"Oinert.

We present an algorithm for efficient computation of the constant term of a power of a multivariate Laurent polynomial. The algorithm is based on univariate interpolation, does not require the storage of intermediate data and can be easily…

In this note we introduce a representation of simple undirected graphs in terms of polynomials and obtain a unique code for a simple undirected graph.

Tensor models are used nowadays for implementing a fundamental theory of quantum gravity. We define here a polynomial $\mathcal T$ encoding the supplementary topological information. This polynomial is a natural generalization of the…

We consider the set of the power non-negative polynomials of several variables and its subset that consists of polynomials which can be represented as a sum of squares. It is shown in the classic work by D.Hilbert that it is a proper…

We discuss numerical solution of Altarelli-Parisi equations in a Laguerre-polynomial method and in a brute-force method. In the Laguerre method, we get good accuracy by taking about twenty Laguerre polynomials in the flavor-nonsinglet case.…

A codeword is associated to a linearized polynomial. The weight distribution of the codewords is determined as the linearized polynomial varies in a family of fixed degree. There is a corresponding result on Wenger graphs from linearized…

Polynomial algebra offers a standard approach to handle several problems in geometric modeling. A key tool is the discriminant of a univariate polynomial, or of a well-constrained system of polynomial equations, which expresses the…

Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we…

Thomassen in 1994 published a famous proof of the fact that the choosability of a planar graph is at most 5. Zhu in 2019 generalized this result by showing that the same bound holds for Alon-Tarsi numbers of planar graphs. We present an…

As one of the first applications of the polynomial method in combinatorics, Alon and Tarsi gave a way to prove that a graph is choosable (colorable from any lists of prescribed size). We describe an efficient way to implement this approach,…