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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

## Valued Abelian Groups

*Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven*

### in Asymptotic Differential Algebra and Model Theory of Transseries

- Published in print:
- 2017
- Published Online:
- October 2017
- ISBN:
- 9780691175423
- eISBN:
- 9781400885411
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175423.003.0003
- Subject:
- Mathematics, Computational Mathematics / Optimization

This chapter deals with valued abelian groups. It first introduces some terminology concerning ordered sets before discussing valued abelian groups and ordered abelian groups in more detail. Ordered ... More

## Moufang Quadrangles

*Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss*

### in Descent in Buildings (AM-190)

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691166902
- eISBN:
- 9781400874019
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691166902.003.0004
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter proves various results about Moufang quadrangles. It first considers the notions of a proper involutory set, a proper indifferent set, and a proper anisotropic pseudo-quadratic space. It ... More

## Statement E Implies Statement D

*Ben Brubaker, Daniel Bump, and Solomon Friedberg*

### in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691150659
- eISBN:
- 9781400838998
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691150659.003.0014
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter introduces the theorem that says Statement E implies Statement D, first by fixing a nodal signature η and presenting a “cut and paste” virtual resotope. It then presents the proof, ... More

## Topological surgery and surgery spaces

*Stanley Chang and Shmuel Weinberger*

### in Quantum Mechanics

- Published in print:
- 2019
- Published Online:
- May 2021
- ISBN:
- 9780691160498
- eISBN:
- 9780691200354
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691160498.003.0004
- Subject:
- Mathematics, Geometry / Topology

This chapter evaluates the fact that the topological (Top) structure set is actually an abelian group and that surgery theory is functorial in the topological category. In doing so, one needs the ... More

## Right-Angled Artin Groups

*Robert W. Bell and 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/9780691158662.003.0014
- Subject:
- Mathematics, Geometry / Topology

This chapter deals with right-angled Artin groups, a broad spectrum of groups that includes free groups on one end, free abelian groups on the other end, and many other interesting groups in between. ... More

## Quantum Chromodynamics

*Michael E. Peskin*

### in Concepts of Elementary Particle Physics

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198812180
- eISBN:
- 9780191850301
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198812180.003.0011
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter introduces non-Abelian gauge symmetry and the associated field equations for spin-1 particles. It proposes the gauge theory Quantum Chromodynamics as the theory of the strong ... More

## Differential-Henselian Fields with Many Constants

*Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven*

### in Asymptotic Differential Algebra and Model Theory of Transseries

- Published in print:
- 2017
- Published Online:
- October 2017
- ISBN:
- 9780691175423
- eISBN:
- 9781400885411
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175423.003.0009
- Subject:
- Mathematics, Computational Mathematics / Optimization

This chapter considers differential-henselian fields with many constants. Here d-henselian includes having small derivation, so d-henselian valued differential fields with many constants are ... 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

## 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

## Relativistic Symmetry

*Kenneth G. Dyall and Knut Faegri*

### in Introduction to Relativistic Quantum Chemistry

- Published in print:
- 2007
- Published Online:
- November 2020
- ISBN:
- 9780195140866
- eISBN:
- 9780197561744
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195140866.003.0011
- Subject:
- Chemistry, Quantum and Theoretical Chemistry

Symmetry is one of the great unifying principles of physics and chemistry. Symmetry governs the geometry of molecules, as well as their spectra and the shapes of their crystals. The symmetry of a ... More

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