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Analytic and Combinatorial Aspects of Certain Identities and Congruences in Partition Theory

2022
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Release : 2022
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Book Synopsis Analytic and Combinatorial Aspects of Certain Identities and Congruences in Partition Theory by : Shreejit Bandyopadhyay

Download or read book Analytic and Combinatorial Aspects of Certain Identities and Congruences in Partition Theory written by Shreejit Bandyopadhyay. This book was released on 2022. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation explores three related topics in the theory of integer partitions. We first revisit certain conjectures made by George Beck about the crank of a partition. We discuss a new approach to these conjectures by decomposing the relevant crank generating function and further explore connections with certain identities involving generalized Lambert series and Appell-Lerch sums. After that, we derive certain weighted generating functions of cranks by both analytic and combinatorial arguments. Lastly, we consider overpartition analogues for Bressoud's generalizations of the famous Rogers-Ramanujan identities. We discuss some new Rogers-Ramanujan type overpartition identities under certain constraints on odd and even parts of the partitions.

The Theory of Partitions

1998-07-28 Mathematics
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Release : 1998-07-28
Genre : Mathematics
Kind : eBook
Book Rating : 664/5 ( reviews)

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Book Synopsis The Theory of Partitions by : George E. Andrews

Download or read book The Theory of Partitions written by George E. Andrews. This book was released on 1998-07-28. Available in PDF, EPUB and Kindle. Book excerpt: Discusses mathematics related to partitions of numbers into sums of positive integers.

Partitions, q-Series, and Modular Forms

2011-11-01 Mathematics
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Release : 2011-11-01
Genre : Mathematics
Kind : eBook
Book Rating : 287/5 ( reviews)

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Book Synopsis Partitions, q-Series, and Modular Forms by : Krishnaswami Alladi

Download or read book Partitions, q-Series, and Modular Forms written by Krishnaswami Alladi. This book was released on 2011-11-01. Available in PDF, EPUB and Kindle. Book excerpt: Partitions, q-Series, and Modular Forms contains a collection of research and survey papers that grew out of a Conference on Partitions, q-Series and Modular Forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions.

Analytic Combinatorics

2009-01-15 Mathematics
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Release : 2009-01-15
Genre : Mathematics
Kind : eBook
Book Rating : 161/5 ( reviews)

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Book Synopsis Analytic Combinatorics by : Philippe Flajolet

Download or read book Analytic Combinatorics written by Philippe Flajolet. This book was released on 2009-01-15. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Analytic And Combinatorial Number Theory: The Legacy Of Ramanujan - Contributions In Honor Of Bruce C. Berndt

2024-08-19 Mathematics
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Release : 2024-08-19
Genre : Mathematics
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Book Rating : 389/5 ( reviews)

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Book Synopsis Analytic And Combinatorial Number Theory: The Legacy Of Ramanujan - Contributions In Honor Of Bruce C. Berndt by : George E Andrews

Download or read book Analytic And Combinatorial Number Theory: The Legacy Of Ramanujan - Contributions In Honor Of Bruce C. Berndt written by George E Andrews. This book was released on 2024-08-19. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois at Urbana-Champaign on June 6-9, 2019. The conference included 26 plenary talks, 71 contributed talks, and 170 participants. As was the case for the conference, this book is in honor of Bruce C Berndt and in celebration of his mathematics and his 80th birthday.Along with a number of papers previously appearing in Special Issues of the International Journal of Number Theory, the book collects together a few more papers, a biography of Bruce by Atul Dixit and Ae Ja Yee, a preface by George Andrews, a gallery of photos from the conference, a number of speeches from the conference banquet, the conference poster, a list of Bruce's publications at the time this volume was created, and a list of the talks from the conference.

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