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Generalized 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/9780195334548.003.0017
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter generalizes Catalan numbers and introduces Fuss numbers.


Divisibility Properties

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/9780195334548.003.0013
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter investigates several divisibility properties of shows Catalan numbers. They include their parity and primality. Mersenne numbers are also described.


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.


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.


A Family of Binary Words

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/9780195334548.003.0015
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter generalizes the family of binary numbers studied in Chapter 5.


Notes on memory (1945)

Alan M. Turing

in Alan Turing's Automatic Computing Engine: The Master Codebreaker's Struggle to build the Modern Computer

Published in print:
2005
Published Online:
January 2008
ISBN:
9780198565932
eISBN:
9780191714016
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198565932.003.0022
Subject:
Mathematics, History of Mathematics

This chapter presents fragments from Turing's draft of ‘Proposed Electronic Calculator’. This material is of interest chiefly because of its remarks concerning the universal machine of Turing's 1936 ... More


Science in the Looking Glass: What Do Scientists Really Know?

E. Brian Davies

Published in print:
2007
Published Online:
September 2008
ISBN:
9780199219186
eISBN:
9780191711695
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219186.001.0001
Subject:
Physics, History of Physics

How do scientific conjectures become laws? Why does proof mean different things in different sciences? Do numbers exist, or were they invented? Why do some laws turn out to be wrong? This book ... 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


Letters-to-Numbers Problems

Patrick R. Laughlin

in Group Problem Solving

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691147918
eISBN:
9781400836673
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147918.003.0006
Subject:
Psychology, Social Psychology

This chapter looks at letters-to-numbers problems, an interesting class of problems that entail many insightful strategies. Letters-to-numbers problems strongly fulfill the four conditions of ... More


General Theorems From Specific Images

Marcus Giaquinto

in Visual Thinking in Mathematics

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199285945
eISBN:
9780191713811
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199285945.003.0008
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter shows that some general arithmetical theorems almost certainly can be discovered by visualizing. First, it describes two examples of what look like acceptable routes to general theorems ... More


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