Overview
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. Thereare 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.
Full Product Details
Author: T. Kyle Petersen
Publisher: Springer-Verlag New York Inc.
Imprint: Springer-Verlag New York Inc.
Edition: 1st ed. 2015
Dimensions:
Width: 15.50cm
, Height: 3.10cm
, Length: 23.50cm
Weight: 9.198kg
ISBN: 9781493930906
ISBN 10: 1493930907
Pages: 456
Publication Date: 13 October 2015
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
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. (Laszlo A. Szekely, zbMATH 1337.05001, 2016)
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. (Laszlo A. Szekely, zbMATH 1337.05001, 2016)
Author Information
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.
