Related papers: Constructing Goeritz matrix from Dehn coloring mat…

In this paper we show that if one writes down the structure equations for the evolution of a curve embedded in an (n)-dimensional Riemannian manifold with constant curvature this leads to a symplectic, a Hamiltonian and an hereditary…

We prove a formula for the structure sheaf of a quiver variety in the Grothendieck ring of its embedding variety. This formula generalizes and gives new expressions for Grothendieck polynomials. We furthermore conjecture that the…

We examine a family of 3-point mappings that include mappings solvable through linearization. The different origins of mappings of this type are examined: projective equations and Gambier systems. The integrable cases are obtained through…

We determine the lens spaces that arise by integer Dehn surgery along a knot in the three-sphere. Specifically, if surgery along a knot produces a lens space, then there exists an equivalent surgery along a Berge knot with the same knot…

In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…

Zarhin showed that a matrix constructed from a polynomial with distinct roots has co-rank one. Some striking properties of this matrix are used to give a direct proof of his result. An account is given of calculations carried out to try to…

This paper shows a polynomial-time algorithm, that given a general matroid $M_1 = (X, \mathcal{I}_1)$ and $k-1$ partition matroids $ M_2, \ldots, M_k$, produces a coloring of the intersection $M = \cap_{i=1}^k M_i$ using at most…

In recent years, a number of fast algorithms for computing the determinant of a Toeplitz matrix were developed. The fastest algorithm we know so far is of order $k^2\log{n}+k^3$, where $n$ is the number of rows of the Toeplitz matrix and…

It is shown that under some additional assumption two diagonalizable integral matrices X and Y with only rational eigenvalues are conjugate in GL(n,Z) if and only if they are conjugate over all localizations. This is used to prove that for…

Node coloring is the task of assigning colors to the nodes of a graph such that no two adjacent nodes have the same color, while using as few colors as possible. It is the most widely studied instance of graph coloring and of central…

We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.…

In many previous papers, the authors used an endomorphism of algebra to twist the original algebraic structures in order to produce the corresponding Hom-algebraic structures. In this works, we use these either a bijective linear map,…

If $E$ is a directed graph, $K$ is a field, and $I$ is a graded ideal of the Leavitt path algebra $L_K(E),$ $I$ is completely determined by an admissible pair $(H,S)$ of two sets of vertices of $E$. The ideal $I=I(H,S)$ is graded isomorphic…

It is well known that the Blanchfield pairing of a knot can be expressed using Seifert matrices. In this paper, we compute the Blanchfield pairing of a colored link with non-zero Alexander polynomial. More precisely, we show that the…

Systems of polynomial equations over the complex or real numbers can be used to model combinatorial problems. In this way, a combinatorial problem is feasible (e.g. a graph is 3-colorable, hamiltonian, etc.) if and only if a related system…

We present the construction of a large class of homogeneous KT, HKT and QKT manifolds, $G/K$, using an invariant metric on $G$ and the canonical connection. For this a decomposition of the Lie algebra of $G$ is employed, which is most…

In this article we give an explicit description of the representation matrix of a Heisenberg type action constructed by Blanchet, Habegger, Masbaum and Vogel. We give the matrix in terms of a ribbon graph and its admissible colorings. We…

Let L_n be the n-dimensional Lorentz cone. A linear map M from R^m to R^n is called Lorentz-positive if M[L_m] is contained in L_n. We extend the notion of concurrence, which was initially introduced to quantify the entanglement of…

Systems of polynomial equations over an algebraically-closed field K can be used to concisely model many combinatorial problems. In this way, a combinatorial problem is feasible (e.g., a graph is 3-colorable, hamiltonian, etc.) if and only…

We compute various types of iterated integrals of Eisenstein-Kronecker forms that are constructed from the Kronecker theta function. Furthermore, we relate the generating series of Gromov-Witten invariants of elliptic curves to these…