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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


Can an ICS Architecture Meet the Systematicity and Productivity Challenges?

Brian P. McLaughlin

in The Architecture of Cognition: Rethinking Fodor and Pylyshyn's Systematicity Challenge

Published in print:
2014
Published Online:
September 2014
ISBN:
9780262027236
eISBN:
9780262322461
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262027236.003.0002
Subject:
Philosophy, Philosophy of Mind

After spelling out the systematicity challenge to connectionism, I examine Paul Smolensky and Géraldine Legendre's attempt to meet the challenge by appeal to a kind of architecture that they label ... More


Classical Analysis

John Stillwell

in Reverse Mathematics: Proofs from the Inside Out

Published in print:
2019
Published Online:
May 2020
ISBN:
9780691196411
eISBN:
9781400889037
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691196411.003.0003
Subject:
Mathematics, History of Mathematics

This chapter explores the basic concepts that arise when real numbers and continuous functions are studied, particularly the limit concept and its use in proving properties of continuous functions. ... More


Graph Theory for Temporal Structure

Jason Yust

in Organized Time: Rhythm, Tonality, and Form

Published in print:
2018
Published Online:
May 2018
ISBN:
9780190696481
eISBN:
9780190696511
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190696481.003.0014
Subject:
Music, Theory, Analysis, Composition

This chapter introduces mathematical graph theory and develops graph-theory concepts that are useful for temporal networks. By generating chord progressions from networks, the potential musical and ... More


The Phase Transition in the Random HornSAT Problem

Demetrios D. Demopoulos and Moshe Y. Vardi

in Computational Complexity and Statistical Physics

Published in print:
2005
Published Online:
November 2020
ISBN:
9780195177374
eISBN:
9780197562260
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195177374.003.0017
Subject:
Computer Science, Mathematical Theory of Computation

This chapter presents a study of the satisfiability of random Horn formulas and a search for a phase transition. In the past decade, phase transitions or sharp thresholds, have been studied ... More


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