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Birkhäuser Advanced Texts Basler Lehrbücher

Eulerian Numbers

Authors: Petersen, T. Kyle

  • Offers a self-contained treatment of progress and problems related to the Eulerian numbers
  • Covers a topic that plays an important role in combinatorics, number theory, and topology
  • Provides previously-unpublished coverage of gamma-nonnegativity of a simplicial complex and its results in combinatorial terms
  • Includes discussion of open problems and directions for future research, as well as numerous exercises and examples
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eBook $59.99
price for USA in USD (gross)
  • ISBN 978-1-4939-3091-3
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  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.99
price for USA in USD
  • ISBN 978-1-4939-3090-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA in USD
  • ISBN 978-1-4939-4794-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group.

The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions.

The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, which survey more advanced topics, including some open problems in combinatorial topology.

This textbook will serve a resource for experts in the field as well as for graduate students and others hoping to learn about these topics for the first time.​

About the authors

T. Kyle Petersen is an Associate Professor of Mathematics at DePaul University, Chicago, USA.  His research areas include algebraic, enumerative, and topological combinatorics.  He received his PhD in Mathematics from Brandeis University.

Reviews

“This book is a beautiful modern collection about Eulerian numbers, which reflects its author's interest and expertise in the subject. The material is rich. Eulerian numbers and their close relatives, such as Narayana numbers, show up in a variety of topics from enumerative, algebraic, topological, and geometric combinatorics. … It is self-contained and presented in a clear ... way. The author describes everything from the basics, so the text should be accessible to a broad audience interested in combinatorics.” (Damir Yeliussizov, Mathematical Reviews, April, 2017)

“This work offers wonderful material to supplement a course in combinatorics or discrete mathematics, or for a stimulating capstone course. Summing Up: Highly recommended. Lower-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 53 (11), July, 2016)

“This book serves dual purposes. On the one hand, it is a monograph on Eulerian numbers and their generalizations. … On the other hand, the book gives an introduction to contemporary enumerative, algebraic and geometric combinatorics, and it can be used as a text at beginning graduate or advanced undergraduate level. … This is a well-written text for a good course.” (László A. Székely, zbMATH 1337.05001, 2016)


Table of contents (14 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-1-4939-3091-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.99
price for USA in USD
  • ISBN 978-1-4939-3090-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA in USD
  • ISBN 978-1-4939-4794-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Eulerian Numbers
Authors
Series Title
Birkhäuser Advanced Texts Basler Lehrbücher
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4939-3091-3
DOI
10.1007/978-1-4939-3091-3
Hardcover ISBN
978-1-4939-3090-6
Softcover ISBN
978-1-4939-4794-2
Series ISSN
1019-6242
Edition Number
1
Number of Pages
XVIII, 456
Number of Illustrations and Tables
74 b/w illustrations, 4 illustrations in colour
Topics