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FOURIER ANALYSIS ON FINITE ABELIAN GROUPS: SOME GRAPHICAL APPLICATIONS

Andrew Goodall

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0007
Subject:
Mathematics, Probability / Statistics

This article reviews basic techniques of Fourier analysis on a finite abelian group Q, with subsequent applications in graph theory. These include evaluations of the Tutte polynomial of a graph G in ... More


Lamplighter Groups

Jennifer Taback

in Office Hours with a Geometric Group Theorist

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691158662
eISBN:
9781400885398
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691158662.003.0015
Subject:
Mathematics, Geometry / Topology

This chapter deals with lamplighter groups. Imagine an infinite main street lined with evenly spaced lamp posts in a rural town. In mathematical terms, the infinite main street may be envisioned as a ... More


and Spaces

Matt Clay and Dan Margalit

in Office Hours with a Geometric Group Theorist

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691158662
eISBN:
9781400885398
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691158662.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter discusses the notion of space, first by explaining what it means for a group to be a group of symmetries of a geometric object. This is the idea of group action, and some examples are ... More


Quasi-isometries

Dan Margalit and Anne Thomas

in Office Hours with a Geometric Group Theorist

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691158662
eISBN:
9781400885398
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691158662.003.0007
Subject:
Mathematics, Geometry / Topology

This chapter considers the notion of quasi-isometry, also known as “coarse isometry.” A whole suite of important algebraic and geometric properties is preserved by quasi-isometries. Quasi-isometry ... More


Asymptotic Dimension

Greg Bell

in Office Hours with a Geometric Group Theorist

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691158662
eISBN:
9781400885398
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691158662.003.0011
Subject:
Mathematics, Geometry / Topology

This chapter considers the notion of asymptotic dimension. It first provides an overview of asymptotic dimension before explaining the asymptotic dimensions of free abelian and nonabelian groups, ... More


Conjugates and Factors

Christophe Reutenauer

in From Christoffel Words to Markoff Numbers

Published in print:
2018
Published Online:
January 2019
ISBN:
9780198827542
eISBN:
9780191866418
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198827542.003.0016
Subject:
Mathematics, Pure Mathematics

Christoffel words are naturally cyclic objects. They may be defined by the Cayley graphs of finite cyclic groups. They have many characterizations through their conjugation classes; among them, one ... More


Automorphisms of Free Groups

Matt Clay

in Office Hours with a Geometric Group Theorist

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691158662
eISBN:
9781400885398
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691158662.003.0006
Subject:
Mathematics, Geometry / Topology

This chapter discusses the automorphisms of free groups. Every group is the collection of symmetries of some object, namely, its Cayley graph. A symmetry of a group is called an automorphism; it is ... More


The Prefix Problem And Its Applications

S. Lakshmivarahan and Sudarshan K. Dhall

in Title Pages

Published in print:
1994
Published Online:
November 2020
ISBN:
9780195088496
eISBN:
9780197560549
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195088496.003.0006
Subject:
Computer Science, Mathematical Theory of Computation

With the emergence of parallel computing, the notion of prefix computation has gained considerable attention in the literature and it plays a central role ... More


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