Locally Finite Planar Edge Transitive Graphs

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Locally Finite, Planar, Edge-Transitive Graphs

Jack E. Graver,Mark E. Watkins
Locally Finite Planar Edge Transitive Graphs Book PDF

Author : Jack E. Graver,Mark E. Watkins
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 50,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821805565

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Locally Finite, Planar, Edge-Transitive Graphs by Jack E. Graver,Mark E. Watkins Pdf

The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected, edge-transitive graphs can be classified according to the number of their end. The 1-ended graphs in this class were identified by Grünbaum and Shephard; Watkins characterized the 2-ended members. Any remaining graphs in this class must have uncountably may ends. In this work, infinite-ended members of this class are shown to exist. A more detailed classification scheme in terms of the types of Petrie walks in the graphs in this class and the local structure of their automorphism groups is presented.

Graph Symmetry

Gena Hahn,Gert Sabidussi
Graph Symmetry Book PDF

Author : Gena Hahn,Gert Sabidussi
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 44,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401589376

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Graph Symmetry by Gena Hahn,Gert Sabidussi Pdf

The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.

Topological Graph Theory

Jonathan L. Gross,Thomas W. Tucker
Topological Graph Theory Book PDF

Author : Jonathan L. Gross,Thomas W. Tucker
Publisher : Courier Corporation
Page : 386 pages
File Size : 45,5 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 9780486417417

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Topological Graph Theory by Jonathan L. Gross,Thomas W. Tucker Pdf

Iintroductory treatment emphasizes graph imbedding but also covers connections between topological graph theory and other areas of mathematics. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem, and examine the genus of a group, including imbeddings of Cayley graphs. Many figures. 1987 edition.

The Structure of $k$-$CS$- Transitive Cycle-Free Partial Orders

Richard Warren
The Structure of k CS Transitive Cycle Free Partial Orders Book PDF

Author : Richard Warren
Publisher : American Mathematical Soc.
Page : 166 pages
File Size : 40,9 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806227

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The Structure of $k$-$CS$- Transitive Cycle-Free Partial Orders by Richard Warren Pdf

The class of cycle-free partial orders (CFPOs) is defined, and the CFPOs fulfilling a natural transitivity assumption, called $k$-connected set transitivity ($k$-$CS$-transitivity), are analyzed in some detail. Classification in many of the interesting cases is given. This work generalizes Droste's classification of the countable $k$-transitive trees ($k \geq 2$). In a CFPO, the structure can branch downwards as well as upwards, and can do so repeatedly (though it never returns to the starting point by a cycle). Mostly it is assumed that $k \geq 3$ and that all maximal chains are finite. The main classification splits into the sporadic and skeletal cases. The former is complete in all cardinalities. The latter is performed only in the countable case. The classification is considerably more complicated than for trees, and skeletal CFPOs exhibit rich, elaborate and rather surprising behavior. Features: Lucid exposition of an important generalization of Droste's work Extended introduction clearly explaining the scope of the memoir Visually attractive topic with copious illustrations Self-contained material, requiring few prerequisites

The Finite Irreducible Linear 2-Groups of Degree 4

Dane Laurence Flannery
The Finite Irreducible Linear 2 Groups of Degree 4 Book PDF

Author : Dane Laurence Flannery
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 52,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821806258

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The Finite Irreducible Linear 2-Groups of Degree 4 by Dane Laurence Flannery Pdf

This memoir contains a complete classification of the finite irreducible 2-subgroups of $GL(4, {\mathbb C})$. Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by a generating set of monomial matrices. The problem is treated by a variety of techniques, including elementary character theory, a method for describing Hasse diagrams of submodule lattices, and calculation of 2-cohomology by means of the Lyndon-Hochschild-Serre spectral sequence. Related questions concerning isomorphism between the listed groups, and Schur indices of their defining characters, are also considered.It's features include: a complete classification of a class of $p$-groups; a first step towards extending presently available databases for use in proposed 'soluble quotient algorithms'; and, groups presented explicitly; may be used to test conjectures or to serve generally as a resource in group-theoretic computations.

Directions in Infinite Graph Theory and Combinatorics

R. Diestel
Directions in Infinite Graph Theory and Combinatorics Book PDF

Author : R. Diestel
Publisher : Elsevier
Page : 128 pages
File Size : 47,7 Mb
Release : 2016-06-06
Category : Mathematics
ISBN : 9781483294797

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Directions in Infinite Graph Theory and Combinatorics by R. Diestel Pdf

This book has arisen from a colloquium held at St. John's College, Cambridge, in July 1989, which brought together most of today's leading experts in the field of infinite graph theory and combinatorics. This was the first such meeting ever held, and its aim was to assess the state of the art in the discipline, to consider its links with other parts of mathematics, and to discuss possible directions for future development. This volume reflects the Cambridge meeting in both level and scope. It contains research papers as well as expository surveys of particular areas. Together they offer a comprehensive portrait of infinite graph theory and combinatorics, which should be particularly attractive to anyone new to the discipline.

Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl
Algebro Geometric Quasi Periodic Finite Gap Solutions of the Toda and Kac van Moerbeke Hierarchies Book PDF

Author : Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 55,9 Mb
Release : 1998
Category : Evolution equations, Nonlinear
ISBN : 9780821808085

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Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies by Wolfgang Bulla,F. Gesztesy,H. Holden,G. Teschl Pdf

In this work, the authors provide a self-contained discussion of all real-valued quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebro-geometric methods, factorization techniques for finite difference expressions, as well as Miura-type transformations. Detailed spectral theoretic properties of Lax pairs and theta function representations of the solutions are derived. Features: Simple and unified treatment of the topic. Self-contained development. Novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.

The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous $n$-tournaments

Gregory L. Cherlin
The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous n tournaments Book PDF

Author : Gregory L. Cherlin
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 50,5 Mb
Release : 1998
Category : Mathematics
ISBN : 0821808362

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The Classification of Countable Homogeneous Directed Graphs and Countable Homogeneous $n$-tournaments by Gregory L. Cherlin Pdf

In this book, Ramsey theoretic methods introduced by Lachlan are applied to classify the countable homogeneous directed graphs. This is an uncountable collection, and this book presents the first explicit classification result covering an uncountable family. The author's aim is to demonstrate the potential of Lachlan's method for systematic use.

Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem

Lawrence C. Evans,Wilfrid Gangbo
Differential Equations Methods for the Monge Kantorovich Mass Transfer Problem Book PDF

Author : Lawrence C. Evans,Wilfrid Gangbo
Publisher : American Mathematical Soc.
Page : 66 pages
File Size : 46,5 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809389

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Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem by Lawrence C. Evans,Wilfrid Gangbo Pdf

In this volume, the authors demonstrate under some assumptions on $f^+$, $f^-$ that a solution to the classical Monge-Kantorovich problem of optimally rearranging the measure $\mu{^+}=f^+dx$ onto $\mu^-=f^-dy$ can be constructed by studying the $p$-Laplacian equation $- \mathrm{div}(\vert DU_p\vert^{p-2}Du_p)=f^+-f^-$ in the limit as $p\rightarrow\infty$. The idea is to show $u_p\rightarrow u$, where $u$ satisfies $\vert Du\vert\leq 1,-\mathrm{div}(aDu)=f^+-f^-$ for some density $a\geq0$, and then to build a flow by solving a nonautonomous ODE involving $a, Du, f^+$ and $f^-$.

Annihilating Fields of Standard Modules of $\mathfrak {sl}(2, \mathbb {C})^\sim $ and Combinatorial Identities

Arne Meurman,Mirko Primc
Annihilating Fields of Standard Modules of mathfrak sl 2 mathbb C sim and Combinatorial Identities Book PDF

Author : Arne Meurman,Mirko Primc
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 41,7 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809235

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Annihilating Fields of Standard Modules of $\mathfrak {sl}(2, \mathbb {C})^\sim $ and Combinatorial Identities by Arne Meurman,Mirko Primc Pdf

In this volume, the authors show that a set of local admissible fields generates a vertex algebra. For an affine Lie algebra $\tilde{\mathfrak g}$, they construct the corresponding level $k$ vertex operator algebra and show that level $k$ highest weight $\tilde{\mathfrak g}$-modules are modules for this vertex operator algebra. They determine the set of annihilating fields of level $k$ standard modules and study the corresponding loop $\tilde{\mathfrak g}$-module--the set of relations that defines standard modules. In the case when $\tilde{\mathfrak g}$ is of type $A^{(1)}_1$, they construct bases of standard modules parameterized by colored partitions, and as a consequence, obtain a series of Rogers-Ramanujan type combinatorial identities.

Relations Related to Betweenness: Their Structure and Automorphisms

Samson Adepoju Adeleke,P. M. Neumann
Relations Related to Betweenness Their Structure and Automorphisms Book PDF

Author : Samson Adepoju Adeleke,P. M. Neumann
Publisher : American Mathematical Soc.
Page : 125 pages
File Size : 44,7 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821806234

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Relations Related to Betweenness: Their Structure and Automorphisms by Samson Adepoju Adeleke,P. M. Neumann Pdf

This volume is about tree-like structures, namely semilinear ordering, general betweenness relations, $C$-relations and $D$-relations. It contains a systematic study of betweenness and introduces $C$ and $D$-relations to describe the behavior of points at infinity ('leaves' or 'ends' or 'directions') of trees. The focus is on structure theorems and on automorphism groups, with applications to the theory of infinite permutation groups. This work: offers the first systematic treatment of betweenness relations; introduces important new concepts of $C$-relations and $D$-relations; elucidates the close relationships between semilinear orderings, betweenness relations, $C$ and $D$-relations; and, considers their automorphism groups as important examples of Jordan permutation groups.

Invariants Under Tori of Rings of Differential Operators and Related Topics

Ian Malcolm Musson,M. van den Bergh
Invariants Under Tori of Rings of Differential Operators and Related Topics Book PDF

Author : Ian Malcolm Musson,M. van den Bergh
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 48,9 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821808856

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Invariants Under Tori of Rings of Differential Operators and Related Topics by Ian Malcolm Musson,M. van den Bergh Pdf

If $G$ is a reductive algebraic group acting rationally on a smooth affine variety $X$, then it is generally believed that $D(X)^G$ has properties very similar to those of enveloping algebras of semisimple Lie algebras. In this book, the authors show that this is indeed the case when $G$ is a torus and $X=k^r\times (k^*)^s$. They give a precise description of the primitive ideals in $D(X)^G$ and study in detail the ring theoretical and homological properties of the minimal primitive quotients of $D(X)^G$. The latter are of the form $B^x=D(X)^G/({\mathfrak g}-\chi({\mathfrak g}))$ where ${\mathfrak g}=\textnormal{Lie}(G)$, $\chi\in {\mathfrak g}^\ast$ and ${\mathfrak g}-\chi({\mathfrak g})$ is the set of all $v-\chi(v)$ with $v\in {\mathfrak g}$. They occur as rings of twisted differential operators on toric varieties. It is also proven that if $G$ is a torus acting rationally on a smooth affine variety, then $D(X[LAMBDA]!/G)$ is a simple ring.

Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders

Lindsay Childs
Hopf Algebras Polynomial Formal Groups and Raynaud Orders Book PDF

Author : Lindsay Childs
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 41,9 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821810774

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Hopf Algebras, Polynomial Formal Groups, and Raynaud Orders by Lindsay Childs Pdf

This book gives two new methods for constructing $p$-elementary Hopf algebra orders over the valuation ring $R$ of a local field $K$ containing the $p$-adic rational numbers. One method constructs Hopf orders using isogenies of commutative degree 2 polynomial formal groups of dimension $n$, and is built on a systematic study of such formal group laws. The other method uses an exponential generalization of a 1992 construction of Greither. Both constructions yield Raynaud orders as iterated extensions of rank $p$ Hopf algebras; the exponential method obtains all Raynaud orders whose invariants satisfy a certain $p$-adic condition.

A Continuum Limit of the Toda Lattice

Percy Deift,Kenneth T-R McLaughlin
A Continuum Limit of the Toda Lattice Book PDF

Author : Percy Deift,Kenneth T-R McLaughlin
Publisher : American Mathematical Soc.
Page : 216 pages
File Size : 54,5 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821806913

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A Continuum Limit of the Toda Lattice by Percy Deift,Kenneth T-R McLaughlin Pdf

In this book, the authors describe a continuum limit of the Toda ODE system, obtained by taking as initial data for the finite lattice successively finer discretizations of two smooth functions. Using the integrability of the finite Toda lattice, the authors adapt the method introduced by Lax and Levermore for the study of the small dispersion limit of the Korteweg de Vries equations to the case of the Toda lattice. A general class of initial data is considered which permits, in particular, the formation of shocks. A novel feature of the analysis in this book is an extensive use of techniques from the theory of Riemann-Hilbert problems.

The Riemann Problem for the Transportation Equations in Gas Dynamics

Wancheng Sheng,Tong Zhang
The Riemann Problem for the Transportation Equations in Gas Dynamics Book PDF

Author : Wancheng Sheng,Tong Zhang
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 45,8 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809471

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The Riemann Problem for the Transportation Equations in Gas Dynamics by Wancheng Sheng,Tong Zhang Pdf

In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which have been merely discussed so far. The generalized Rankine-Hugoniot and entropy conditions for Dirac delta waves are clarified with viscous vanishing method. All of the existence, uniqueness and stability for viscous perturbations are proved analytically.