## A Family of Binary Words

*Thomas Koshy*

### in Catalan Numbers with Applications

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0015
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter generalizes the family of binary numbers studied in Chapter 5.

## Tribinomial Coefficients

*Thomas Koshy*

### in Catalan Numbers with Applications

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0016
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter extends the definition of a binomial coefficient using triangular numbers. In the process, Hermite's divisibility properties, Hoggatt–Hansell identity, and Catalan numbers are visited. ... More

## Thiele: Pioneer in Statistics

*Steffen L. Lauritzen*

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198509721
- eISBN:
- 9780191709197
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509721.001.0001
- Subject:
- Mathematics, Probability / Statistics

Thorvald Nicolai Thiele was a brilliant Danish researcher of the 19th century. He was a professor of Astronomy at the University of Copenhagen and the founder of Hafnia, the first Danish private ... More

## Binomial Coefficients

*Thomas Koshy*

### in Catalan Numbers with Applications

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents a brief introduction to binomial coefficients, the cornerstone of all the discussions in the book. Among the properties discussed are Hermite's divisibility properties. Catalan ... More

## The Central Binomial Coefficient

*Thomas Koshy*

### in Catalan Numbers with Applications

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0002
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter focuses on the ubiquitous central binomial coefficient and its properties. It confirms that Cn is a positive integer. The chapter covers Lagrange's identity.

## The Central Binomial Coefficient Revisited

*Thomas Koshy*

### in Catalan Numbers with Applications

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0003
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter continues to investigate the central binomial coefficient in much greater detail. Topics explained include Wallis' product, Lucas numbers, Fermat's little theorem, Carlitz's formula, ... More

## INTRODUCTION

*Mathew Penrose*

### in Random Geometric Graphs

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198506263
- eISBN:
- 9780191707858
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506263.003.0001
- Subject:
- Mathematics, Probability / Statistics

This introductory chapter contains a general discussion of both the historical and the applied background behind the study of random geometric graphs. A brief overview is presented, along with some ... More

## BEGINNING OF THE PRO-SUBJECTIVE APPROACH

*Shoutir Kishore Chatterjee*

### in Statistical Thought: A Perspective and History

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198525318
- eISBN:
- 9780191711657
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525318.003.0007
- Subject:
- Mathematics, Probability / Statistics

Around the middle of the 18th century, Bayes conceived the idea of treating an unknown parameter as a subjective random variable distributed according to a prior, and inferring about it from its ... More

## Regression with a Count Dependent Variable Regression with a Count Dependent Variable

*John G. Orme and Terri Combs-Orme*

### in Multiple Regression with Discrete Dependent Variables

- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780195329452
- eISBN:
- 9780199864812
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195329452.003.0005
- Subject:
- Social Work, Research and Evaluation

Count variables indicate the number of times a particular event occurs to each case, usually within some domain of observation such as a given time period, population size, or geographical area. This ... More

## Introduction

*Bernhard Wälchli*

### in Co-Compounds and Natural Coordination

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780199276219
- eISBN:
- 9780191706042
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199276219.003.0001
- Subject:
- Linguistics, Syntax and Morphology

This chapter introduces co-compounds and their basic formal, semantic, and use-oriented (distributional) properties, as well as tight coordination patterns, such as bare binomials, which have in ... More

## Evaluating Deficit Patterns of Broca Aphasics in the Presence of High Intersubject Variability

*Dan Drai*

### in Broca's Region

- Published in print:
- 2006
- Published Online:
- May 2009
- ISBN:
- 9780195177640
- eISBN:
- 9780199864799
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195177640.003.0007
- Subject:
- Neuroscience, Sensory and Motor Systems, Behavioral Neuroscience

A hypothesis about the existence of a computation for which Broca's area is indispensable would take the following form: identify two classes of sentences such that one involves the relevant ... More

## The Binomial Model

*Tomas Björk*

### in Arbitrage Theory in Continuous Time

- Published in print:
- 2004
- Published Online:
- October 2005
- ISBN:
- 9780199271269
- eISBN:
- 9780191602849
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199271267.003.0002
- Subject:
- Economics and Finance, Financial Economics

This chapter discusses the binomial model — the simplest nontrivial model of a financial market. It begins with the period version of the model, then the model is extended to an arbitrary number of ... More

## A More General One period Model

*Tomas Björk*

### in Arbitrage Theory in Continuous Time

- Published in print:
- 2004
- Published Online:
- October 2005
- ISBN:
- 9780199271269
- eISBN:
- 9780191602849
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199271267.003.0003
- Subject:
- Economics and Finance, Financial Economics

This chapter examines the absence of arbitrage and completeness in slightly more general terms than in the binomial model. Although a one period model is considered, the financial market and the ... More

## Random Variables

*James Davidson*

### in Stochastic Limit Theory: An Introduction for Econometricians

- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198774037
- eISBN:
- 9780191596117
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774036.003.0008
- Subject:
- Economics and Finance, Econometrics

Specializing the concepts of Ch. 7 to the case of real variables, this chapter introduces distribution functions, discrete and continuous distributions, and describes examples such as the binomial, ... More

## Probability

*Stephen J. Blundell and Katherine M. Blundell*

### in Concepts in Thermal Physics

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter defines some basic concepts in probability theory. It begins by stating that the probability of occurrence of a particular event, taken from a finite set of possible events, is zero if ... More

## PROBABILITY THEORY

*Robert M. Mazo*

### in Brownian Motion: Fluctuations, Dynamics, and Applications

- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199556441
- eISBN:
- 9780191705625
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556441.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter begins with a review of elementary probability theory, conditional probability, and statistical independence. It explains the notion of a random variable and its distribution function or ... More

## Can Organizational Mechanisms Solve Minority Group Coordination Problems? Logic, Lessons, and Evidence from Legislative Caucuses in the American States

*Kristin Kanthak and George A. Krause*

### in The Diversity Paradox: Parties, Legislatures, and the Organizational Foundations of Representation in America

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199891726
- eISBN:
- 9780199933433
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199891726.003.0006
- Subject:
- Political Science, American Politics

This chapter explores the use of legislative member organizations, or caucuses, as catalysts for the type of coordination that was shown in the previous chapter to be beneficial for minority group ... More

## The arithmetical triangle

*A. W. F. EDWARDS*

### 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/9780199656592.003.0008
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

The arithmetical triangle is the most famous of all number patterns. Apparently a simple listing of the binomial coefficients, it contains the triangular and pyramidal numbers of ancient Greece, the ... More

## . Ray, Linnaeus, and the Ordering of the World

*John G. T. Anderson*

### in Deep Things out of Darkness: A History of Natural History

- Published in print:
- 2012
- Published Online:
- January 2014
- ISBN:
- 9780520273764
- eISBN:
- 9780520954458
- Item type:
- chapter

- Publisher:
- University of California Press
- DOI:
- 10.1525/california/9780520273764.003.0007
- Subject:
- Biology, Natural History and Field Guides

In which natural history leaves behind its medieval phase and becomes a modern science. John Ray develops a more systemic taxonomy using trinomial Latin descriptions of plants and animals, a system ... More

## The Legal Language of Scottish Burghs: Standardization and Lexical Bundles (1380-1560)

*Joanna Kopaczyk*

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199945153
- eISBN:
- 9780199345939
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199945153.001.0001
- Subject:
- Linguistics, Sociolinguistics / Anthropological Linguistics, English Language

The book offers an innovative, corpus-driven approach to historical legal discourse. It is the first monograph to examine textual standardization patterns in legal and administrative texts on the ... More