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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


A Method of Modal Proof In Aristotle

Jacob Rosen and Marko Malink

in Oxford Studies in Ancient Philosophy: Volume 42

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199644384
eISBN:
9780191743344
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199644384.003.0006
Subject:
Philosophy, Ancient Philosophy

In Prior Analytics 1. 15, Aristotle states the following rule of modal logic, which we may call the possibility rule: given the premiss that A is possible, and given a derivation of B from A, it can ... 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


Conclusion of the Proof

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0017
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents the tools to prove that the proof of Theorem 1.2 is reduced to Statement G. It begins with the lemma stating that the cardinality of each Γ‎-pack or Δ‎-pack is a power of 2. It ... More


On some concepts of infinite divisibility and their roles in turbulence, finance and quantum stochastics

Ole Eiler Barndorff-Nielsen

in Celebrating Statistics: Papers in honour of Sir David Cox on his 80th birthday

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566540
eISBN:
9780191718038
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566540.003.0013
Subject:
Mathematics, Probability / Statistics

This chapter contains an account of contemporary Lévy theory, namely the theory of infinite divisibility, Lévy processes, Lévy bases, and so forth, which has been a very active area of research over ... More


Concurrence

Ben Brubaker, Daniel Bump, and Solomon Friedberg

in Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.003.0016
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents purely combinatorial results that are needed for the proof of Statement G. The motivation for these results comes from the appearance of divisibility conditions through the ... More


Making Nothing of “Almighty Space”

Paul Russell

in The Riddle of Hume's Treatise: Skepticism, Naturalism, and Irreligion

Published in print:
2008
Published Online:
May 2008
ISBN:
9780195110333
eISBN:
9780199872084
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195110333.003.0009
Subject:
Philosophy, History of Philosophy

This chapter argues that one of Hume's principal objectives in his discussion of space and time is to discredit the Newtonian doctrine of absolute space and time, which had recently been given a ... More


Aristotle's Refinements of Plato's Theory

Kathrin Koslicki

in The Structure of Objects

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199539895
eISBN:
9780191716300
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199539895.003.0007
Subject:
Philosophy, Metaphysics/Epistemology, Ancient Philosophy

This chapter examines Aristotle's refinements of Plato's theory of composition. Aristotle is generally sympathetic to the Platonic outlook, but differs over the details. In some cases, Aristotle's ... More


Kant's Justification of the Laws of Mechanics

Eric Watkins

in Kant and the Sciences

Published in print:
2001
Published Online:
February 2006
ISBN:
9780195133059
eISBN:
9780199786169
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195133056.003.0008
Subject:
Philosophy, Philosophy of Science

This paper notes a number of differences between Newton’s formulations of the laws of motion and Kant’s formulations of the laws of mechanics, and then argues that these differences are not ... More


The Evolution of Resource Property Rights

Anthony Scott

Published in print:
2008
Published Online:
May 2008
ISBN:
9780198286035
eISBN:
9780191718410
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198286035.001.0001
Subject:
Economics and Finance, Development, Growth, and Environmental

This book reacts to an economic literature which relies on theory to explain property rights. To correct this truistic approach the book traces the actual evolution by examining when, where, and how ... More


Homogeneity and flexibility in temporal modification *

Aniko Csirmaz

in Merging Features: Computation, Interpretation, and Acquisition

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199553266
eISBN:
9780191720833
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199553266.003.0013
Subject:
Linguistics, Syntax and Morphology, Theoretical Linguistics

Following an overview of time intervals in the clause, this chapter tackles the appropriate characterization of divisibility, the requirement of durative adverbs which can measure any of these times. ... More


The syntactically well‐behaved comparative correlative *

Heather Lee Taylor

in Merging Features: Computation, Interpretation, and Acquisition

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199553266
eISBN:
9780191720833
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199553266.003.0014
Subject:
Linguistics, Syntax and Morphology, Theoretical Linguistics

Following an overview of time intervals in the clause, this chapter tackles the appropriate characterization of divisibility — the requirement of durative adverbs which can measure any of these ... More


Aristotle: The Formal Analysis of Spatial Magnitude and Locomotion

Michael J. White

in The Continuous and the Discrete: Ancient Physical Theories from a Contemporary Perspective

Published in print:
1992
Published Online:
October 2011
ISBN:
9780198239529
eISBN:
9780191679940
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198239529.003.0001
Subject:
Philosophy, Ancient Philosophy, Philosophy of Science

This chapter focuses on Aristotle's formal, structural analysis of spatial magnitude and locomotion. It analyses spatial magnitude and motion in terms of their geometrical or topological properties. ... More


The Architecture of Matter: Galileo to Kant

Thomas Holden

Published in print:
2004
Published Online:
January 2005
ISBN:
9780199263264
eISBN:
9780191601743
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0199263264.001.0001
Subject:
Philosophy, History of Philosophy

Examines the debate in early modern philosophy over the composition and internal architecture of matter, focussing on problems concerning the structure of continua, the metaphysics of parts and ... More


Quantity and Continuity

Richard Cross

in The Physics of Duns Scotus: The Scientific Context of a Theological Vision

Published in print:
1998
Published Online:
October 2011
ISBN:
9780198269748
eISBN:
9780191683787
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198269748.003.0007
Subject:
Religion, Philosophy of Religion, Theology

This chapter explains how Scotus conceives of a body's position. A common view is that a body's extension is closely connected with the space that the ... More


Aggregation and Two Moral Methods

F. M. Kamm

in Intricate Ethics: Rights, Responsibilities, and Permissible Harm

Published in print:
2007
Published Online:
October 2011
ISBN:
9780195189698
eISBN:
9780199851096
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195189698.003.0003
Subject:
Philosophy, Moral Philosophy

This chapter explores whether the number of people we can help counts morally in deciding what to do in conflict situations when we cannot help everyone. It begins by reconsidering the arguments of ... More


Hume and Berkeley on the Proofs of Infinite Divisibility

Robert J. Fogelin

in Philosophical Interpretations

Published in print:
1992
Published Online:
November 2003
ISBN:
9780195071627
eISBN:
9780199833221
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019507162X.003.0004
Subject:
Philosophy, General

Berkeley, and Hume following him, rejected the doctrine that lines, e.g., are infinitely divisible. They both thought that the notion of infinite divisibility lead to paradoxical results. To avoid ... More


Leibniz Arrives at Monads

Jonathan Bennett

in Learning from Six Philosophers Volume 1

Published in print:
2001
Published Online:
November 2003
ISBN:
9780198250913
eISBN:
9780191597053
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198250916.003.0013
Subject:
Philosophy, History of Philosophy

Leibniz held that there are no material substances (because of divisibility), and that there are immaterial substances, which he called ‘monads’. They are absolutely real; bodies are appearances of ... More


Mating Horses with Griffins: the Problems of Material Structure

Thomas Holden

in The Architecture of Matter: Galileo to Kant

Published in print:
2004
Published Online:
January 2005
ISBN:
9780199263264
eISBN:
9780191601743
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199263264.003.0001
Subject:
Philosophy, History of Philosophy

As figures such as Hume, Bayle, Leibniz, and Kant emphasized, an array of paradoxes threatened early modern accounts of the structure of matter. Presents an organizing survey of these paradoxes, and ... More


The Actual Parts Doctrine and Shortcircuit Arguments

Thomas Holden

in The Architecture of Matter: Galileo to Kant

Published in print:
2004
Published Online:
January 2005
ISBN:
9780199263264
eISBN:
9780191601743
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199263264.003.0003
Subject:
Philosophy, History of Philosophy

According to the actual parts doctrine, all the parts into which a material body can be divided exist as so many independent beings. Various early modern philosophers argued that this entails that ... More


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