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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.


Needles in a Haystack: the Class NP

Cristopher Moore and Stephan Mertens

in The Nature of Computation

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199233212
eISBN:
9780191775079
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233212.003.0004
Subject:
Physics, Theoretical, Computational, and Statistical Physics

NP refers to a class of decision problems in which yes-instances are easy to verify. That is: a decision problem is in NP if, whenever the answer for a particular instance is ‘yes’, there is a simple ... More


Randomized Algorithms

Cristopher Moore and Stephan Mertens

in The Nature of Computation

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199233212
eISBN:
9780191775079
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233212.003.0010
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Certain situations require a random rather than a deterministic strategy. With a random strategy, the choices are unpredictable and the adversary may be kept off balance. This chapter focuses on the ... More


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