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Pascal' Triangle and Catalan Numbers

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/9780195334548.003.0012
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter shows the various ways Catalan numbers can be extracted from Pascal's triangle. It includes discussion of nonisomorphic groups, Catalan polynomials, Touchard's recursive formula, and ... More


A Catalan Triangle

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/9780195334548.003.0014
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter investigates an interesting triangular array that contains Catalan numbers and Cayley numbers.


The International Politics of EU-China Relations

Liu Fei

David Kerr (ed.)

Published in print:
2007
Published Online:
January 2012
ISBN:
9780197264089
eISBN:
9780191734809
Item type:
book
Publisher:
British Academy
DOI:
10.5871/bacad/9780197264089.001.0001
Subject:
Political Science, International Relations and Politics

The European Union and China have emerged as new international actors. They have an increasingly diverse relationship covering the economy, politics, technology, culture and education; but beyond ... More


Matching between impaired and intact fields

L. Weiskrantz

in Blindsight: A Case Study and Implications

Published in print:
1990
Published Online:
January 2008
ISBN:
9780198521921
eISBN:
9780191706226
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198521921.003.0014
Subject:
Psychology, Cognitive Neuroscience

Given the good discrimination in the blind field, the question arises as to whether it is processed differently than discriminations in the intact field. One way of addressing the question was to ... More


Catalan Numbers with Applications

Thomas Koshy

Published in print:
2008
Published Online:
January 2009
ISBN:
9780195334548
eISBN:
9780199868766
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195334548.001.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

Fibonacci and Lucas sequences are “two shining stars in the vast array of integer sequences,” and because of their ubiquitousness, tendency to appear in quite unexpected and unrelated places, ... 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


Tress and Catalan Numbers

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/9780195334548.003.0008
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents delightful occurrences of Catalan numbers in the theory of trees. They include binary trees, full binary trees, planted trivalent binary trees, triangulations and prefix ... More


Shifting Global Networks and the Development of a New International Hierarchy of Firms and Supplier Countries

Christel Lane and Jocelyn Probert

in National Capitalisms, Global Production Networks: Fashioning the Value Chain in the UK, US, and Germany

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199214815
eISBN:
9780191721779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199214815.003.0006
Subject:
Business and Management, International Business, Political Economy

This chapter discusses first sub-regional economic activity and the use of so-called ‘triangle manufacturing’ in Asia as a response to the quota system. This practice explains the emergence of new ... More


The Problem of Disease When Domesticating Bees

Rosalind R. James

in Bee Pollination in Agricultural Ecosystems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780195316957
eISBN:
9780199871575
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195316957.003.0008
Subject:
Biology, Animal Biology, Plant Sciences and Forestry

When disease strikes a hive of bees, it can devastate the colony and spread to the entire beekeeping operation. All bees are susceptible to diseases, and when they are domesticated, their population ... More


MONADS AND ALGEBRAS

Steve Awodey

in Category Theory

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568612
eISBN:
9780191717567
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568612.003.0010
Subject:
Mathematics, Algebra

This chapter presents a third characterization of adjunctions. This one has the virtue of being entirely equational. Topics discussed include the triangle identities, monads and adjoints, algebras ... More


‘Form’ discrimination

L. Weiskrantz

in Blindsight: A Case Study and Implications

Published in print:
1990
Published Online:
January 2008
ISBN:
9780198521921
eISBN:
9780191706226
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198521921.003.0008
Subject:
Psychology, Cognitive Neuroscience

D. B.'s ability to discriminate shapes by forced-choice guessing was studied using various letters, rectangles vs. squares, and degrees of curvature of triangles. Both projected and back-illuminated ... More


Standard situation

L. Weiskrantz

in Blindsight: A Case Study and Implications

Published in print:
1990
Published Online:
January 2008
ISBN:
9780198521921
eISBN:
9780191706226
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198521921.003.0017
Subject:
Psychology, Cognitive Neuroscience

During the last few years of work with D. B., it became possible to test a number of subjects with visual field defects at the National Hospital in London using a standard set of visual tests. The ... More


Mapping the representative claim

Michael Saward

in The Representative Claim

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199579389
eISBN:
9780191722950
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199579389.003.0003
Subject:
Political Science, Political Theory

This chapter defines and elaborates a number of key aspects of the representative claim, underscoring the latter's distinctive utility as an analytical tool. After locating the representative claim ... More


The North Atlantic Triangle: Economic Reconstruction and Collapse, 1923–1933

Volker R. Berghahn

in American Big Business in Britain and Germany: A Comparative History of Two "Special Relationships" in the 20th Century

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161099
eISBN:
9781400850297
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161099.003.0005
Subject:
History, American History: 20th Century

This chapter deals with the period between the 1923 economic crisis and an even more severe economic breakdown in 1929. This period saw an engagement of the United States in Europe that had not been ... More


Postmobilization Romance: Transforming Military Rejection into Modernist Tragedy and Symbolism

Keith Gandal

in The Gun and the Pen: Hemingway, Fitzgerald, Faulkner and the Fiction of Mobilization

Published in print:
2008
Published Online:
September 2008
ISBN:
9780195338911
eISBN:
9780199867127
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195338911.003.0006
Subject:
Literature, Criticism/Theory, American, 20th Century Literature

These three authors, although compulsively writing out of a distress engendered by their “mobilization wounds,” learned by the time of writing their twenties masterpieces to submerge and transfigure ... More


Riemann Surfaces, Coverings, and Hypergeometric Functions

Paula Tretkoff

in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.003.0003
Subject:
Mathematics, Geometry / Topology

This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and ... More


The North Atlantic Business Triangle and the Constellation of 1900–1901

Volker R. Berghahn

in American Big Business in Britain and Germany: A Comparative History of Two "Special Relationships" in the 20th Century

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161099
eISBN:
9781400850297
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161099.003.0002
Subject:
History, American History: 20th Century

This chapter begins the story of the American–British–German business and political relationship in the year 1900. It assesses the prevailing attitudes toward this transitional period in terms of ... More


Advancing the Concept of Public Goods

Inge Kaul and Ronald U. Mendoza

in Providing Global Public Goods: Managing Globalization

Published in print:
2003
Published Online:
November 2003
ISBN:
9780195157406
eISBN:
9780199832965
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195157400.003.0004
Subject:
Economics and Finance, Public and Welfare

Examines the implications of translating the concept of public goods, originally developed in the setting of a domestic national economy, to that of global public goods set within a transnational ... More


How Analysis and Synthesis are Related

Kurt Smith

in Matter Matters: Metaphysics and Methodology in the Early Modern Period

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199583652
eISBN:
9780191723155
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199583652.003.0013
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

This chapter shows how the combinatorial nature of bodies expresses the permutation group concept, the latter expressing the conditions underwriting a genuine mathematical system. The chapter ... More


Country Soul: Making Music and Making Race in the American South

Charles L. Hughes

Published in print:
2015
Published Online:
January 2016
ISBN:
9781469622439
eISBN:
9781469623245
Item type:
book
Publisher:
University of North Carolina Press
DOI:
10.5149/northcarolina/9781469622439.001.0001
Subject:
History, African-American History

In the sound of the 1960s and 1970s, nothing symbolized the rift between black and white America better than the seemingly divided genres of country and soul. Yet the music emerged from the same ... More


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