Related papers: A Witt type formula
We introduce the concept of weight graph for the weight system $P\frak{g}(T)$ of a finite dimensional nilpotent Lie algebra $\frak{g}$ and analyze the necessary conditions for a $(p,q)$-graph to be a weight graph for some $\frak{g}$.
This paper constructs a combinatorial model for all postcritically finite rational maps arising as the Newton's method of a complex polynomial. This model is used in [LMS] to give a combinatorial classification of postcritically finite…
A multi-relational graph maintains two or more relations over a vertex set. This article defines an algebra for traversing such graphs that is based on an $n$-ary relational algebra, a concatenative single-relational path algebra, and a…
Hecke algebras are beautiful q-extensions of Coxeter groups. In this paper, we prove several results on their characters, with an emphasis on characters induced from trivial and sign representations of parabolic subalgebras. While most of…
We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as…
I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss…
We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point purely in terms of the original Hamiltonian, avoiding the normalization procedure.…
In this paper we explore a new method of analysis of associative algebras.
We define a zeta function woth respect to the twisted Grover matrix of a mixed digraph, and present an exponential expression and a determinant expression of this zeta function. As an application, we give a trace formula with respect to the…
This is the first part of a 2 part survey on the functor of the big and p-adic Witt vectors.
We study the properties of certain graphs involving the sums of primes. Their structure largely turns out to relate to the distribution of prime gaps and can be roughly seen in Cram\'er's model as well. We also discuss generalizations to…
We give an elementary proof of an interesting combinatorial identity which is of particular interest in graph theory and its applications. Two applications to enumeration of forests with closed-form expressions are given.
The aim of this note is to give a formula expressing the trace form associated with the 27 lines of a cubic surface.
The goal of the paper is to establish cubature formulas on combinatorial graphs. Two types of cubature formulas are developed. Cubature formulas of the first type are exact on spaces of variational splines on graphs. Since badlimited…
In this talk, we are concerned with the formulation and understanding of the combinatorics of time-ordered n-point functions in terms of the Hopf algebra of field operators. Mathematically, this problem can be formulated as one in…
In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…
In this paper we provide an algebraic derivation of the explicit Witten volume formulas for a few semi-simple Lie algebras by combining a combinatorial method with the ideas used by Gunnells and Sczech in computation of higher-dimensional…
We present new combinatorial insights into the calculation of (Castelnuovo-Mumford) regularity of graphs.
This paper surveys some combinatorial aspects of Smith normal form, and more generally, diagonal form. The discussion includes general algebraic properties and interpretations of Smith normal form, critical groups of graphs, and Smith…
The determinants of modular Collatz graphs and the modular Conway amusical permutation graph are determined, and some interesting number theoretic properties are described.