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Partitions 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/9780195334548.003.0010
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter investigates several occurrences of Catalan numbers in the theory of partitioning. Noncrossing partition is explained in detail.


EXPANDING THE TUTTE POLYNOMIAL OF A MATROID OVER THE INDEPENDENT SETS

Koko Kalambay Kayibi

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/9780198571278.003.0011
Subject:
Mathematics, Probability / Statistics

This chapter provides direct combinatorial proof of an expansion of the Tutte polynomial by independent sets of the matroid. Another expansion of the Tutte polynomial is presented in terms of ... More


A Game-Theoretic Perspective on Coalition Formation

Debraj Ray

Published in print:
2007
Published Online:
January 2008
ISBN:
9780199207954
eISBN:
9780191709104
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199207954.001.0001
Subject:
Economics and Finance, Financial Economics

The formation of coalitions to achieve both collaborative and competitive goals is a phenomenon we see all around us. The list of examples of this phenomenon is long and varied: production cartels, ... More


The Limits to Coercive Consociationalism in Northern Ireland

John McGarry and Brendan O'Leary

in The Northern Ireland Conflict: Consociational Engagements

Published in print:
2004
Published Online:
August 2004
ISBN:
9780199266579
eISBN:
9780191601446
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199266573.003.0003
Subject:
Political Science, UK Politics

The chapter, initially published in 1989, reviews efforts by the UK and Irish governments to achieve a settlement in Northern Ireland during the late 1980s. It bears the impress of its time; ... More


THE HIGH NOON OF UNIONISM: 1886–1921

Iain Mclean and Alistair McMillan

in State of the Union

Published in print:
2005
Published Online:
February 2006
ISBN:
9780199258208
eISBN:
9780191603334
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199258201.003.0005
Subject:
Political Science, UK Politics

This chapter examines the unravelling of the Union between 1886 and 1921. It discusses the continuing link between Union and Empire, the incoherence of Diceyan Unionism, centre-periphery politics, ... More


Parts of the Soul

Hendrik Lorenz

in The Brute Within: Appetitive Desire in Plato and Aristotle

Published in print:
2006
Published Online:
September 2006
ISBN:
9780199290635
eISBN:
9780191604027
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199290636.003.0003
Subject:
Philosophy, Ancient Philosophy

This chapter raises and explains two central questions about Plato’s theory of the tripartite soul. First, what is involved in Plato’s claim that the embodied human soul is a thing of parts? ... More


The Argument for Tripartition

Hendrik Lorenz

in The Brute Within: Appetitive Desire in Plato and Aristotle

Published in print:
2006
Published Online:
September 2006
ISBN:
9780199290635
eISBN:
9780191604027
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199290636.003.0004
Subject:
Philosophy, Ancient Philosophy

This chapter argues that Republic-style partition of the soul amounts to a position that can fairly be characterized in terms of two main claims. First, the proper subjects of desires and aversions ... More


Partition

Hendrik Lorenz

in The Brute Within: Appetitive Desire in Plato and Aristotle

Published in print:
2006
Published Online:
September 2006
ISBN:
9780199290635
eISBN:
9780191604027
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199290636.003.0005
Subject:
Philosophy, Ancient Philosophy

This chapter addresses the concern that for a Platonic soul to make sense, is not right to say that it has genuine parts. It also assesses the philosophical cost of soul-partition by considering its ... More


Organizational Ecology as a Theory of Competition

Nikolaus Beck

in The Institutions of the Market: Organizations, Social Systems, and Governance

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199231423
eISBN:
9780191710865
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199231423.003.0010
Subject:
Business and Management, Political Economy

This chapter shows that organizational ecology is much more sociological and less biological than many critics of organizational ecology think. It argues that organizational ecology and its theory of ... More


Advanced Statistical Mechanics

Barry M McCoy

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199556632
eISBN:
9780191723278
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556632.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book begins where elementary books and courses leave off and covers the advances made in statistical mechanics in the past fifty years. The book is divided into three parts. The first part is on ... More


The Tenability of Partition as a Mode of Conflict Regulation: Comparing Ireland With Palestine–Land of Israel

Sammy Smooha

in Northern Ireland and the Divided World: Post-Agreement Northern Ireland in Comparative Perspective

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199244348
eISBN:
9780191599866
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199244340.003.0013
Subject:
Political Science, UK Politics

Smooha argues that Jews have settled in Palestine – Land of Israel in sufficient strength to establish a strong independent state in part of the area (pre‐1967 Israel), although their attempt to ... More


Relativistic gases

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/9780199562091.003.0025
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter repeats the derivation of the partition function for a gas, and hence of the other thermodynamic properties that can be obtained from it, but this time includes relativistic effects. It ... More


Senior Officials in the German Federal Administration: Institutional Change and Positional Differentiation

Klaus H. Goetz

in Bureaucratic Elites in Western European States: A Comparative Analysis of Top Officials

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198294467
eISBN:
9780191600067
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198294468.003.0008
Subject:
Political Science, Comparative Politics

This account of institutional change and positional differentiation of senior officials in Germany's Federal administration is presented in five sections. Section I, ‘Senior Officials and the ... More


Resizing and Reshaping the State: India from Partition to the Present

Gurharpal Singh

in Right-sizing the State: The Politics of Moving Borders

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199244904
eISBN:
9780191600050
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199244901.003.0005
Subject:
Political Science, Comparative Politics

Gurharpal Singh traces the institutional dependence of the Indian state on conceptions of itself and its original borders as sacrosanct. But, the author argues that the state is, in reality, reshaped ... More


The analysis of biodiversity experiments: from pattern toward mechanism

Andy Hector, Thomas Bell, John Connolly, John Finn, Jeremy Fox, Laura Kirwan, Michel Loreau, Jennie McLaren, Bernhard Schmid, and Alexandra Weigelt

in Biodiversity, Ecosystem Functioning, and Human Wellbeing: An Ecological and Economic Perspective

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199547951
eISBN:
9780191720345
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199547951.003.0007
Subject:
Biology, Ecology, Biodiversity / Conservation Biology

Meta-analysis of the first generation of biodiversity experiments has revealed that there is a general positive relationship between diversity and ecosystem processes that is consistent across ... More


The Structure of Experience

Barbara Tversky, Jeffrey M. Zacks, and Bridgette Martin Hard

in Understanding Events: From Perception to Action

Published in print:
2008
Published Online:
May 2008
ISBN:
9780195188370
eISBN:
9780199870462
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195188370.003.0019
Subject:
Psychology, Cognitive Neuroscience

This chapter focuses on the structure of experience, covering language, objects, scenes, and events. It is argued that partitioning the world is the first step to comprehending it. Some partitioning ... More


TESTING FOR THE EXISTENCE OF HOMOMORPHISMS

Pavol Hell and Jaroslav Nešetřil

in Graphs and Homomorphisms

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528173
eISBN:
9780191713644
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528173.003.0005
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter explores the algorithmic aspects of graph homomorphisms and of similar partition problems. The highlights include the dichotomy classification of graph homomorphisms to a fixed target ... More


SEGMENTATION PROBLEMS

Andrea Braides

in Gamma-Convergence for Beginners

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198507840
eISBN:
9780191709890
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507840.003.0006
Subject:
Mathematics, Applied Mathematics

The study of segmentation problems, i.e., variational problems where the unknown is a piecewise-constant function, allows the introduction of a new type of weak convergence, related to the weak* ... More


FLOWS AND FERROMAGNETS

Geoffrey Grimmett

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/9780198571278.003.0008
Subject:
Mathematics, Probability / Statistics

The Tutte polynomial and its relatives play important roles in matroid theory, computational complexity, and models of statistical physics. They provide the natural way to count and relate a variety ... More


SUBSTRUCTURE LATTICES

Roman Kossak and James H. Schmerl

in The Structure of Models of Peano Arithmetic

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568278
eISBN:
9780191718199
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568278.003.0004
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter examines substructure lattices, with emphasis on how to obtain models with specific finite lattices as substructure lattices. The finite distributive lattice case is presented in full. ... More


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