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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


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