Skip to main content

Brandon Allen

North Dakota State University, Mathematics, Graduate Student

Winona State University, Mathematics and Philosophy, Undergraduate

Followers

55

Following

18

Public Views

In Mathematics, I have a strong interest in Algberaic Combinatorics with an emphasis in Coxeter Theory concerning Automata. In particular, combinatorial applications of the Brink-Howlett automaton for irreducible Coxeter groups. My biggest contribution is giving an explicit algorithmic way to calculate characteristic polynomials for affine irreducible Coxeter groups that give another way to put an upper-bound on the chromatic number for a given Coxeter group. I am currently composing a manuscript on providing a non-trivial lowerbound, and upper bound for the closed coefficient problem for the polynomials of reduced words of length n.

M.S. Mathematics - North Dakota State University Mathematics Department (Fall 2022)
B.S. Mathematics, Philosophy minor- Winona State University. (Spring 2016)
Supervisors: Dr. Azer Akhmedov, Dr. Debnath, and Joyati
Phone: 15072161639
Address: 304 31st Ave N
203

less

Christophe Hohlweg

Université du Québec à Montréal

Brian Sarzosa Zuleta

Escuela Politecnica del Ejercito (ESPE) Ecuador

Henrik Eriksson

KTH Royal Institute of Technology

Northern Arizona University

Université du Québec à Montréal

Cristian Lenart

University of Salento

University of Maryland, College Park

Nathan Williams

University of California, Santa Barbara

InterestsView All (9)

Uploads

Papers by Brandon Allen

Enumeration of Reduced Words of Length n for Coxeter Groups via Brink-Howlett Automaton (Official Masters Paper)

The overall goal of this paper is to give a method of computing out how many words of length $n$ ... more The overall goal of this paper is to give a method of computing out how many words of length $n$ there are for any Coxeter group via its Brink-Howlett automaton. \cite{BH93} \cite{Brink} To build our automaton, we focus on Coxeter systems and root systems honing in on a special set of roots called the small roots. We follow closely \cite{Ardila} \cite{BB05} for the first two chapters. Finally, we build the Brink-Howlett automaton through literature compiled through the years and present explicit examples of $\tilde{A_1}$ and the Coxeter group on three generators which each pair of generators is in a free relation with one another.\cite{HNW} \cite{Yau} \cite{YauThesis}

Can Fichte's Philosophy Handle Category Theory and Topology?(HOM-SIGMAA 2016 Paper)

This document describes the relationship of Mathematics and Philosophy in Fichte’s text The Vocat... more

Fichtean Mathematical Egoism

This document describes the relationship of Mathematics and Philosophy in Fichte's text The Vocat... more This document describes the relationship of Mathematics and Philosophy in Fichte's text The Vocation of Man. This paper will explore the possibilities of Platonism in Fichte's theory, Fichte's theory of measurement, theory of space, and transition in space in regards to substance and attributes. This paper proposes a new outlook onto Fichte's philosophy by using elementary Topology. This paper shall go over the problems of using Fichtean theory of consciousness as a mathematical entity and how Fichte backs against these arguments.

Bluffing in Simplified Poker Game

A simpliﬁed poker game is analyzed with comparison against theoretical and experimental results b... more A simpliﬁed poker game is analyzed with comparison against theoretical and experimental results both from literature and experimental sources. Mixed-strategy Nash equilibrium and signaling strategies are discussed in the theoretical aspect as well as complications using theoretical modeling. Applications that are derived from this poker game can give insight into how government and people cooperate with ﬁnancial services.

Dirichlet Problem: Introduction

provides an insight for undergraduates to tackle Dirichlet's problem at an undergraduate level un... more

Fichte's Determinism by Nature

This paper looks at the problem of Determinism that Fichte faces in "The Vocation of Man". We exp... more This paper looks at the problem of Determinism that Fichte faces in "The Vocation of Man". We explore some ways in which nature's determinism plays a direct effect into the human consciousness in the view of Fichte. We also compare how his dealing with determinism is different than the Early Modern Philosophers.

Philosophy of Nothing

This paper takes a look at the concept nothingness through the Early Modern Era and the refutatio... more This paper takes a look at the concept nothingness through the Early Modern Era and the refutations against these arguments. This paper evaluates the preconceived notions of upholding the rejection of nothingness for two centuries until the 1990's came about with the school of Metaphysical Nihilists. In 2000's this school of thought was refuted against and was seen to be brought down. I come up with a new theory about the world being made out of infinitesimals by using radical Pythagorean theory, in which nothing could maybe exist in the end run if the universe is an ultrafilter.

Drafts by Brandon Allen

Cluster Algebras For the Brink-Howlett Automaton

The Brink-Howlett automaton is a combinatorial tool created in 1993 to enumerate the reduced word... more The Brink-Howlett automaton is a combinatorial tool created in 1993 to enumerate the reduced words of length n for a given Coxeter group. [2] Current research for the Brink-Howlett Automaton has focused in the field area of Automata Theory. [7] This paper will give motivations as to study the Brink-Howlett automaton cluster algebras of a fixed Coxeter system. The overall goal of this paper is to give a new perspective on cluster algebras of the Brink-Howlett automaton of Coxeter groups.

Brink-Howlett Automation in Coordination with Matroid Theory

The goal of this paper is to prove the log-concavity conjecture for irreducible Coxeter groups, b... more

Forming Unique Plane Partitions of an element in S

Forming plane partitions out of an element of S_n and S_n^{B}. We are inspired by an exercise fro... more

ISOMETRIES OF H

The goal of this paper is obtain a correspondence between the matrices of SL 2 (R) and the isomet... more The goal of this paper is obtain a correspondence between the matrices of SL 2 (R) and the isometries of the hyperbolic plane. This paper inspects mainly Kathy Snyder's paper theorems and definitions.[8] We first start of by defining the hyperbolic plane and then move onto defining what it means to be a translation, dilation and rotation and see how all three are isometries of the hyperbolic plane. Through a construction of an action in accordance with the Mobius transformation we achieve by looking at the properties of SL 2 (R) the translation, dilation and rotation matrix. We then question and answer if it is possible to determine give an arbitrary 2 x 2 matrix if its a translation, rotation or dilation.

Enumeration of Reduced Words of Length n for Coxeter Groups via Brink-Howlett Automaton (Official Masters Paper)

The overall goal of this paper is to give a method of computing out how many words of length $n$ ... more The overall goal of this paper is to give a method of computing out how many words of length $n$ there are for any Coxeter group via its Brink-Howlett automaton. \cite{BH93} \cite{Brink} To build our automaton, we focus on Coxeter systems and root systems honing in on a special set of roots called the small roots. We follow closely \cite{Ardila} \cite{BB05} for the first two chapters. Finally, we build the Brink-Howlett automaton through literature compiled through the years and present explicit examples of $\tilde{A_1}$ and the Coxeter group on three generators which each pair of generators is in a free relation with one another.\cite{HNW} \cite{Yau} \cite{YauThesis}

Can Fichte's Philosophy Handle Category Theory and Topology?(HOM-SIGMAA 2016 Paper)

This document describes the relationship of Mathematics and Philosophy in Fichte’s text The Vocat... more

Fichtean Mathematical Egoism

This document describes the relationship of Mathematics and Philosophy in Fichte's text The Vocat... more This document describes the relationship of Mathematics and Philosophy in Fichte's text The Vocation of Man. This paper will explore the possibilities of Platonism in Fichte's theory, Fichte's theory of measurement, theory of space, and transition in space in regards to substance and attributes. This paper proposes a new outlook onto Fichte's philosophy by using elementary Topology. This paper shall go over the problems of using Fichtean theory of consciousness as a mathematical entity and how Fichte backs against these arguments.

Bluffing in Simplified Poker Game

A simpliﬁed poker game is analyzed with comparison against theoretical and experimental results b... more A simpliﬁed poker game is analyzed with comparison against theoretical and experimental results both from literature and experimental sources. Mixed-strategy Nash equilibrium and signaling strategies are discussed in the theoretical aspect as well as complications using theoretical modeling. Applications that are derived from this poker game can give insight into how government and people cooperate with ﬁnancial services.

Dirichlet Problem: Introduction

provides an insight for undergraduates to tackle Dirichlet's problem at an undergraduate level un... more

Fichte's Determinism by Nature

This paper looks at the problem of Determinism that Fichte faces in "The Vocation of Man". We exp... more This paper looks at the problem of Determinism that Fichte faces in "The Vocation of Man". We explore some ways in which nature's determinism plays a direct effect into the human consciousness in the view of Fichte. We also compare how his dealing with determinism is different than the Early Modern Philosophers.

Philosophy of Nothing

This paper takes a look at the concept nothingness through the Early Modern Era and the refutatio... more This paper takes a look at the concept nothingness through the Early Modern Era and the refutations against these arguments. This paper evaluates the preconceived notions of upholding the rejection of nothingness for two centuries until the 1990's came about with the school of Metaphysical Nihilists. In 2000's this school of thought was refuted against and was seen to be brought down. I come up with a new theory about the world being made out of infinitesimals by using radical Pythagorean theory, in which nothing could maybe exist in the end run if the universe is an ultrafilter.

Cluster Algebras For the Brink-Howlett Automaton

The Brink-Howlett automaton is a combinatorial tool created in 1993 to enumerate the reduced word... more The Brink-Howlett automaton is a combinatorial tool created in 1993 to enumerate the reduced words of length n for a given Coxeter group. [2] Current research for the Brink-Howlett Automaton has focused in the field area of Automata Theory. [7] This paper will give motivations as to study the Brink-Howlett automaton cluster algebras of a fixed Coxeter system. The overall goal of this paper is to give a new perspective on cluster algebras of the Brink-Howlett automaton of Coxeter groups.

Brink-Howlett Automation in Coordination with Matroid Theory

The goal of this paper is to prove the log-concavity conjecture for irreducible Coxeter groups, b... more

Forming Unique Plane Partitions of an element in S

Forming plane partitions out of an element of S_n and S_n^{B}. We are inspired by an exercise fro... more

ISOMETRIES OF H

The goal of this paper is obtain a correspondence between the matrices of SL 2 (R) and the isomet... more The goal of this paper is obtain a correspondence between the matrices of SL 2 (R) and the isometries of the hyperbolic plane. This paper inspects mainly Kathy Snyder's paper theorems and definitions.[8] We first start of by defining the hyperbolic plane and then move onto defining what it means to be a translation, dilation and rotation and see how all three are isometries of the hyperbolic plane. Through a construction of an action in accordance with the Mobius transformation we achieve by looking at the properties of SL 2 (R) the translation, dilation and rotation matrix. We then question and answer if it is possible to determine give an arbitrary 2 x 2 matrix if its a translation, rotation or dilation.