We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to give a state sum formula for the twisted Alexander polynomial of a knot depending on a representation of the knot group.

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

A new model for representing PD-induced relations that are derived from DAGrepresentable relations through marginalization over a subset of their variables is introduced. The new model requires polynomial space and a polynomial algorithm is given for testing whether a given triplet is represented in the model. In addition a polynomial algorithm is derived for testing whether a marginalized DAGr...

ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...

The algebra of monodromy matrices for sl(n) trigonometric R-matrix is studied. It is shown that a generic finite-dimensional polynomial irreducible representation of this algebra is equivalent to a tensor product of L-operators. Cocommutativity of representations is discussed and inter-twiners for factorizable representations are written through the Boltzmann weights of the sl(n) chiral Potts m...

‎    The Narumi-Katayama index is the first topological index defined by the product of some graph theoretical quantities. Let G be a simple graph. Narumi-Katayama index of G is defined as the product of the degrees of the vertices of G. In this paper, we define the Narumi-Katayama polynomial of G. Next, we investigate some properties of this polynomial for graphs and then, we obtain ...

in this paper, trajectory generation for the 4 dof arm of surena iii humanoid robot with the purpose of optimizing energy and avoiding a moving obstacle is presented. for this purpose, first, kinematic equations for a seven dof manipulator are derived. then, using the lagrange method, an explicit dynamics model for the arm is developed. in the next step, in order to generate the desired traject...

Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...