Istvan Mezo

Combinatorics and Number Theory of Counting Sequences (eBook, ePUB)

• Format: ePub

Produktbeschreibung

Combinatorialists are seldom aware of number theoretical tools, and number theorists rarely aware of possible combinatorial applications. This book is accessible for both of the groups. The first part introduces important counting sequences. The second part shows how these sequences can be generalized to study new combinatorial problems

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 498
• Erscheinungstermin: 19. August 2019
• Englisch
• ISBN-13: 9781351346375
• Artikelnr.: 57501901

Autorenporträt

István Mezo is a Hungarian mathematician. He obtained his PhD in 2010 at the University of Debrecen. He was working in this institute until 2014. After two years of Prometeo Professorship at the Escuela Politécnica Nacional (Quito, Ecuador) between 2012 and 2014 he moved to Nanjing, China, where he is now a full-time research professor.

Inhaltsangabe

I Counting sequences related to set partitions and permutations

Set partitions and permutation cycles.

Generating functions

The Bell polynomials

Unimodality, log concavity and log convexity

The Bernoulli and Cauchy numbers

Ordered partitions

Asymptotics and inequalities

II Generalizations of our counting sequences

Prohibiting elements from being together

Avoidance of big substructures

Prohibiting elements from being together

Avoidance of big substructures

Avoidance of small substructures

III Number theoretical properties

Congurences

Congruences vial finite field methods

Diophantic results

Appendix

Rezensionen

This book provides an interesting introduction to combinatorics by employing number-theoretic techniques of counting sequences. The level of the presentation often seems elementary, as the author frequently throws out lagniappes suitable for high school students. The text unfolds in three parts. Part 1 covers set partitions, generating functions, Bell polynomials, log-concavity, log-convexity, Bernoulli and Cauchy numbers, ordered partitions, asymptotes, and related inequalities. Part 2 discusses generalizations of counting sequences in three chapters. The final part considers number theoretical properties, including congruences, by way of finite field methods and Diophantine results. Each chapter concludes with an "Outlook" section that gives suggestions about exploring additional topics not covered in the text. Mathematical proof is used throughout the exposition and tends to be "enumerative," again contributing to a sense that the author hopes to engage mathematical novices through this text. However, the more than 250 exercises included in the book are frequently challenging and always interesting. The bibliography comprises more than 600 entries. Anyone who can follow the text is likely to enjoy working through the book.
-D. P. Turner, Faulkner University