## Graphs and Homomorphisms

*Pavol Hell and Jaroslav Nesetril*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528173
- eISBN:
- 9780191713644
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528173.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. This text is devoted entirely to the subject, bringing ... More

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

*Geoffrey Grimmett and Colin McDiarmid (eds)*

- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780198571278
- eISBN:
- 9780191718885
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198571278.001.0001
- Subject:
- Mathematics, Probability / Statistics

Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation. He has taught, influenced, and ... More

## The Mathematics of Various Entertaining Subjects: Research in Games, Graphs, Counting, and Complexity, Volume 2

*Jason Rosenhouse and Jennifer Beineke (eds)*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691171920
- eISBN:
- 9781400889136
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691171920.001.0001
- Subject:
- Mathematics, History of Mathematics

The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, ... More

## Combinatorics: Ancient and Modern

*Robin Wilson and John J. Watkins (eds)*

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to ... More

## From Christoffel Words to Markoff Numbers

*Christophe Reutenauer*

- Published in print:
- 2018
- Published Online:
- January 2019
- ISBN:
- 9780198827542
- eISBN:
- 9780191866418
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198827542.001.0001
- Subject:
- Mathematics, Pure Mathematics

Christoffel introduced in 1875 a special class of words on a binary alphabet, linked to continued fractions. Some years laterMarkoff published his famous theory, called nowMarkoff theory. It ... More

## Constructivist Theories of Ethnic Politics

*Kanchan Chandra (ed.)*

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199893157
- eISBN:
- 9780199980079
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199893157.001.0001
- Subject:
- Political Science, Comparative Politics

The book is motivated by a disjuncture in social science research on ethnicity, politics and economics: Although theories of the formation of ethnic groups are driven by the constructivist assumption ... More

## Random Tensors

*Răzvan Gheorghe Gurău*

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198787938
- eISBN:
- 9780191829918
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198787938.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Particle Physics / Astrophysics / Cosmology

This book presents a self-contained, ab initio introduction to random tensors. The book is divided into two parts. The first part introduces the general framework and the main results on random ... More

## Introduction

*Kanchan Chandra*

### in Constructivist Theories of Ethnic Politics

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199893157
- eISBN:
- 9780199980079
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199893157.003.0001
- Subject:
- Political Science, Comparative Politics

This chapter provides a complete sketch of the key concepts and arguments introduced in this book as well as the stakes attached to each. It introduces the conceptual framework for thinking about ... More

## Mathematics in Hebrew in Medieval Europe

*Roi Wagner, Naomi Aradi, Avinoam Baraness, David Garber, Stela Segev, Shai Simonson, Ilana Wartenberg, Menso Folkerts, Barnabas Hughes, Roi Wagner, and J. Lennart Berggren*

*Victor J. Katz (ed.)*

### in Sourcebook in the Mathematics of Medieval Europe and North Africa

- Published in print:
- 2016
- Published Online:
- January 2018
- ISBN:
- 9780691156859
- eISBN:
- 9781400883202
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691156859.003.0003
- Subject:
- Mathematics, History of Mathematics

This chapter covers mathematics written in Hebrew between the eleventh and sixteenth centuries in Europe. It starts with the practical and scholarly—as well as earlier and later—Hebrew expositions of ... More

## Two Case Studies of Semiosis in Mathematics

*Roi Wagner*

### in Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780691171715
- eISBN:
- 9781400883783
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691171715.003.0005
- Subject:
- Mathematics, History of Mathematics

This chapter presents two case studies that highlight the problems of mathematical semiosis: how mathematical signs obtain and change their senses. The first case study follows the paradigmatic ... More

## Enumeration (18th–20th centuries)

*E. KEITH LLOYD*

### in Combinatorics: Ancient and Modern

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.003.0013
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

By the end of the 18th century, what is now called ‘enumerative combinatorics’ was emerging as a distinct discipline. The connections between certain combinatorial problems and algebraical expansions ... More

## A Personal View of Combinatorics

*PETER J. CAMERON*

### in Combinatorics: Ancient and Modern

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.003.0016
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

This chapter presents a quick overview of the recent development of combinatorics and its current directions — as a discipline in its own right, as a part of mathematics and, more generally, as a ... More

## Lying Side by Side: Fitting Color to Eros

*Barbara Maria Stafford*

### in Ribbon of Darkness: Inferencing from the Shadowy Arts and Sciences

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780226630489
- eISBN:
- 9780226630656
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226630656.003.0003
- Subject:
- Philosophy, Philosophy of Mind

Carnal knowledge contravenes body/mind dualism. The repetitive horizontal inlay presents an ancient binding format relying on compressed color as an invitation to sensory response. This essay argues ... More

## From Communicable Matter to Incommunicable “Stuff”: Extreme Combinatorics and the Return of Ineffability

*Barbara Maria Stafford*

### in Ribbon of Darkness: Inferencing from the Shadowy Arts and Sciences

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780226630489
- eISBN:
- 9780226630656
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226630656.003.0006
- Subject:
- Philosophy, Philosophy of Mind

Since Kant, there has been an intense debate around the question of the location of the Sublime: Is it in the object or in the subject? This essay tackles ineffability’s dark side: the fast-growing, ... More

## Two Thousand Years of Combinatorics

*DONALD E. KNUTH*

### in Combinatorics: Ancient and Modern

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.003.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

Early work on the generation of combinatorial patterns began as civilization itself was taking shape. The story is quite fascinating, and we will see that it spans many cultures in many parts of the ... More

## Free Groups and Folding

*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/9780691158662.003.0004
- Subject:
- Mathematics, Geometry / Topology

This chapter studies subgroups of free groups using the combinatorics of graphs and a simple operation called folding. It introduces a topological model for free groups and uses this model to show ... More

## Prosodic status of morphemes in the lexicon: stress

*Tomas Riad*

### in The Phonology of Swedish

- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199543571
- eISBN:
- 9780191747168
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199543571.003.0010
- Subject:
- Linguistics, Phonetics / Phonology, Language Families

A major theme of this book is the lexcial specification of prosodic information, and the consequences that this has for the understanding of word formation and the shape of the lexicon in Swedish. It ... More

## Reconstructing Random Jigsaws

*Paul Balister, Béla Bollobás, and Bhargav Narayanan*

### in Multiplex and Multilevel Networks

- Published in print:
- 2018
- Published Online:
- December 2018
- ISBN:
- 9780198809456
- eISBN:
- 9780191847073
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198809456.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The chapter “Reconstructing Random Jigsaws” examines the reconstruction problem for a family of discrete structures, asking whether it is possible to uniquely reconstruct a structure in this family ... More

## Free probability

*Alice Guionnet*

### in Stochastic Processes and Random Matrices: Lecture Notes of the Les Houches Summer School: Volume 104, July 2015

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198797319
- eISBN:
- 9780191838774
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198797319.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Free probability was introduced by D. Voiculescu as a theory of noncommutative random variables (similar to integration theory) equipped with a notion of freeness very similar to independence. In ... More

## The Probabilistic Turn (1876–1884)

*Olivier Darrigol*

### in Atoms, Mechanics, and Probability: Ludwig Boltzmann's Statistico-Mechanical Writings - An Exegesis

- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198816171
- eISBN:
- 9780191853661
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198816171.003.0005
- Subject:
- Physics, Atomic, Laser, and Optical Physics, History of Physics

This chapter deals with writings in which Boltzmann expressed the statistical nature of the entropy law and temporarily made the relation between entropy and combinatorial probability a basic ... More