Related papers: Goeritz and Seifert Matrices from Dehn Presentatio…
In this article, we shall derive by elementary calculations the Gauss map, spherical image, Weingarten map and the curvatures at identity of the special linear group, that is, the matrices of determinant 1. We could not find any reference…
It is shown that an undirected graph $G$ is cospectral with the Hermitian adjacency matrix of a mixed graph $D$ obtained from a subgraph $H$ of $G$ by orienting some of its edges if and only if $H=G$ and $D$ is obtained from $G$ by a…
The generalized distance matrix of a graph is a matrix in which the $(i,j)$th entry is a function, $f$, of the distance between vertex $i$ and vertex $j$. Depending on the choice of $f$, this family of matrices includes both the adjacency…
We introduce a concept of similarity between vertices of directed graphs. Let G_A and G_B be two directed graphs. We define a similarity matrix whose (i, j)-th real entry expresses how similar vertex j (in G_A) is to vertex i (in G_B. The…
The eccentricity matrix $\epsilon(G)$, of a connected graph $G$ is obtained by retaining the maximum distance from each row and column of the distance matrix of $G$ and the other entries are assigned with 0. In this paper, we discuss the…
The inverse of the metric matrices on the Siegel-Jacobi upper half space ${\mathcal{X}}^J_n$, invariant to the restricted real Jacobi group $G^J_n(\mathbb{R})_0$ and extended Siegel-Jacobi $\tilde{{\mathcal{X}}}^J_n$ upper half space,…
Using a generating function approach, the correlation coefficients of four different graph-theoretical indices, namely the number of independent vertex subsets, the number of matchings, the number of subtrees and the Wiener index, are…
Let G be a graph with undirected and directed edges. Its representation is given by assigning a vector space to each vertex, a bilinear form on the corresponding vector spaces to each directed edge, and a linear map to each directed edge.…
The Jacobi system on a full-line lattice is considered when it contains additional weight factors. A factorization formula is derived expressing the scattering from such a generalized Jacobi system in terms of the scattering from its…
All order Seiberg--Witten maps of gauge parameter, gauge field and matter fields are given as a closed recursive formula. These maps are obtained by analyzing the order by order solutions of the gauge consistency and equivalence conditions…
We explain how Gaussian integrals over ensemble of complex matrices with source matrices generate Hurwitz numbers of the most general type, namely, Hurwitz numbers with arbitrary orientable or non-orientable base surface and arbitrary…
We reduce some key calculations of compositions of morphisms between Soergel bimodules ("Soergel calculus") to calculations in the nil Hecke ring ("Schubert calculus"). This formula has several applications in modular representation theory.
For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types…
Let $G$ be a connected graph on $n$ vertices and $D(G)$ its distance matrix. The formula for computing the determinant of this matrix in terms of the number of vertices is known when the graph is either a tree or {a} unicyclic graph. In…
We describe a graphical model for probabilistic relationships---an alternative to the Bayesian network---called a dependency network. The graph of a dependency network, unlike a Bayesian network, is potentially cyclic. The probability…
The theory of generalized locally Toeplitz (GLT) sequences was conceived as an apparatus for computing the spectral distribution of matrices arising from the numerical discretization of differential equations (DEs). The purpose of this…
A theory of orientation on gain graphs (voltage graphs) is developed to generalize the notion of orientation on graphs and signed graphs. Using this orientation scheme, the line graph of a gain graph is studied. For a particular family of…
We present a simple, but efficient, way to calculate connection matrices between sets of independent local solutions, defined at two neighboring singular points, of Fuchsian differential equations of quite large orders, such as those found…
General Fierz-type identities are examined and their well known connection with completeness relations in matrix vector spaces is shown. In particular, I derive the chiral Fierz identities in a simple and systematic way by using a chiral…
We obtain a presentation of Schur algebras (and q-Schur algebras) by generators and relations which is compatible with the usual presentation of the enveloping algebra (quantized enveloping algebra) corresponding to the Lie algebra gl(n) of…