Related papers: A combinatorial introduction to Adinkras
We discuss the mechanism by which adinkras holographically store the required information for the Spin(1,3) Clifford Algebra fiber bundle in the cases of three 4D, N=1 representations: the chiral, vector and tensor supermultiplets.
Recent work on classicication of off-shell representations of N-extended worldline supersymmetry without central charges has uncovered an unexpectedly vast number--trillions of even just (chromo)topology types--of so called adinkraic…
This manuscript synthesizes almost fifteen years of research in algebraic combinatorics, in order to highlight, theme by theme, its perspectives. In part one, building on my thesis work, I use tools from commutative algebra, and in…
Presented in this paper the nature of the supersymmetrical representation theory behind 4D, N = 1 theories, as described by component fields, is investigated using the tools of Adinkras and Garden Algebras. A survey of familiar matter…
A division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division…
Algebraic realizations of supersymmetry through SU(m,n) type superalgebras are developed. We show their applications to a bilocal quark-antiquark or a quark-diquark systems. A new scheme based on SU(6/1) is fully exploited and the bilocal…
For a star-shaped graph, we introduce special characters and study their properties. We decompose special characters into odd and even parts and study their evolution under reflections. We apply the obtained formulas to prove that the…
Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…
In this thesis, we study connections between metric and combinatorial graphs from a Dirichlet space point of view.
Graph-structured combinatorial challenges are inherently difficult due to their nonlinear and intricate nature, often rendering traditional computational methods ineffective or expensive. However, these challenges can be more naturally…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…
This paper describes a unified method solving for inverse, forward, and hybrid dynamics problems for robotic manipulators with either open kinematic chains or closed kinematic loops based on factor graphs. Manipulator dynamics is considered…
Cadabra is a new computer algebra system designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification taking care of Bianchi and Schouten identities, for…
In the context of signed line graphs, this article introduces a modified inflation technique to study strong Gram congruence of non-negative (integral quadratic) unit forms, and uses it to show that weak and strong Gram congruence coincide…
We continue the development of a theory of off-shell supersymmetric representations analogous to that of compact Lie algebras such as SU(3). For off-shell 4D, N = 1 systems, quark-like representations have been identified [1] in terms of…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible…
This paper develops the theory of KLR algebras with a Dynkin diagram automorphism. This is foundational material intended to allow folding techniques in the theory of KLR algebras.
The Dunkl--Dirac operator is a deformation of the Dirac operator by means of Dunkl derivatives. We investigate the symmetry algebra generated by the elements supercommuting with the Dunkl--Dirac operator and its dual symbol. This symmetry…