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Articles 1 - 11 of 11
Full-Text Articles in Discrete Mathematics and Combinatorics
Strong Homotopy Lie Algebras And Hypergraphs, Samuel J. Bevins, Marco Aldi
Strong Homotopy Lie Algebras And Hypergraphs, Samuel J. Bevins, Marco Aldi
Undergraduate Research Posters
We study hypergraphs by attaching a nilpotent strong homotopy Lie algebra. We especially focus on hypergraph theoretic information that is encoded in the cohomology of the resulting strong homotopy Lie algebra.
Counting The Moduli Space Of Pentagons On Finite Projective Planes, Maxwell Hosler
Counting The Moduli Space Of Pentagons On Finite Projective Planes, Maxwell Hosler
Senior Independent Study Theses
Finite projective planes are finite incidence structures which generalize the concept of the real projective plane. In this paper, we consider structures of points embedded in these planes. In particular, we investigate pentagons in general position, meaning no three vertices are colinear. We are interested in properties of these pentagons that are preserved by collineation of the plane, and so can be conceived as properties of the equivalence class of polygons up to collineation as a whole. Amongst these are the symmetries of a pentagon and the periodicity of the pentagon under the pentagram map, and a generalization of …
Categorical Aspects Of Graphs, Jacob D. Ender
Categorical Aspects Of Graphs, Jacob D. Ender
Undergraduate Student Research Internships Conference
In this article, we introduce a categorical characterization of directed and undirected graphs, and explore subcategories of reflexive and simple graphs. We show that there are a number of adjunctions between such subcategories, exploring varying combinations of graph types.
On The Mysteries Of Interpolation Jack Polynomials, Havi Ellers
On The Mysteries Of Interpolation Jack Polynomials, Havi Ellers
HMC Senior Theses
Interpolation Jack polynomials are certain symmetric polynomials in N variables with coefficients that are rational functions in another parameter k, indexed by partitions of length at most N. Introduced first in 1996 by F. Knop and S. Sahi, and later studied extensively by Sahi, Knop-Sahi, and Okounkov-Olshanski, they have interesting connections to the representation theory of Lie algebras. Given an interpolation Jack polynomial we would like to differentiate it with respect to the variable k and write the result as a linear combination of other interpolation Jack polynomials where the coefficients are again rational functions in k. In this …
The Automorphism Group Of The Halved Cube, Benjamin B. Mackinnon
The Automorphism Group Of The Halved Cube, Benjamin B. Mackinnon
Theses and Dissertations
An n-dimensional halved cube is a graph whose vertices are the binary strings of length n, where two vertices are adjacent if and only if they differ in exactly two positions. It can be regarded as the graph whose vertex set is one partite set of the n-dimensional hypercube, with an edge joining vertices at hamming distance two. In this thesis we compute the automorphism groups of the halved cubes by embedding them in R n and realizing the automorphism group as a subgroup of GLn(R). As an application we show that a halved cube is a circulant graph if …
Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus
Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus
Electronic Theses and Dissertations
The manufacturer claims that there is only one solution to the puzzle Instant Insanity II. However, a recent paper shows that there are two solutions. Our goal is to find ways in which we only have one solution. We examine the permutation groups of the puzzle and use modern algebra to attempt to fix the puzzle. First, we find the permutation group for the case when there is only one empty slot at the top. We then examine the scenario when we add an extra column or an extra row to make the game a 4 × 5 puzzle or …
Polynomial Factoring Algorithms And Their Computational Complexity, Nicholas Cavanna
Polynomial Factoring Algorithms And Their Computational Complexity, Nicholas Cavanna
Honors Scholar Theses
Finite fields, and the polynomial rings over them, have many neat algebraic properties and identities that are very convenient to work with. In this paper we will start by exploring said properties with the goal in mind of being able to use said properties to efficiently irreducibly factorize polynomials over these fields, an important action in the fields of discrete mathematics and computer science. Necessarily, we must also introduce the concept of an algorithm’s speed as well as particularly speeds of basic modular and integral arithmetic opera- tions. Outlining these concepts will have laid the groundwork for us to introduce …
Algebraic Structures On Fuzzy Unit Square And Neutrosophic Unit Square, Florentin Smarandache, W.B. Vasantha Kandasamy
Algebraic Structures On Fuzzy Unit Square And Neutrosophic Unit Square, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors build algebraic structures on fuzzy unit semi open square UF = {(a, b) | a, b [0, 1)} and on the fuzzy neutrosophic unit semi open square UN = {a + bI | a, b [0, 1)}. This study is new and we define, develop and describe several interesting and innovative theories about them. We cannot build ring on UN or UF. We have only pseudo rings of infinite order. We also build pseudo semirings using these semi open unit squares. We construct vector spaces, S-vector spaces and strong pseudo special vector space using …
Algebraic Structures On Real And Neutrosophic Semi Open Squares, Florentin Smarandache, W.B. Vasantha Kandasamy
Algebraic Structures On Real And Neutrosophic Semi Open Squares, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Here for the first time we introduce the semi open square using modulo integers. Authors introduce several algebraic structures on them. These squares under addition modulo ‘n’ is a group and however under product this semi open square is only a semigroup as under the square has infinite number of zero divisors. Apart from + and we define min and max operation on this square. Under min and max operation this semi real open square is a semiring. It is interesting to note that this semi open square is not a ring under + and since …
The Rook-Brauer Algebra, Elise G. Delmas
The Rook-Brauer Algebra, Elise G. Delmas
Mathematics, Statistics, and Computer Science Honors Projects
We introduce an associative algebra RBk(x) that has a basis of rook-Brauer diagrams. These diagrams correspond to partial matchings on 2k vertices. The rook-Brauer algebra contains the group algebra of the symmetric group, the Brauer algebra, and the rook monoid algebra as subalgebras. We show that the basis of RBk(x) is generated by special diagrams si, ti (1 <= i < k) and pj (1 <= j <= k), where the si are the simple transpositions that generated the symmetric group Sk, the ti are the "contraction maps" which generate the …
N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
With the advent of computers one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure namely n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of nvector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several …