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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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