Eulerian Numbers

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.

“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)

• Eulerian Numbers.- Narayana Numbers.- Partially Ordered Sets.- Gamma-nonnegativity.- Weak Order, Hyperplane Arrangements, and the Tamari Lattice.- Refined Enumeration.- Simplicial Complexes.- Barycentric Subdivision.- Coxeter Groups.- W-Narayana Numbers.- Cubes, Carries, and an Amazing Matrix.- Characterizing f-vectors.- Combinatorics for Coxeter groups of Types Bn and Dn.- Affine Descents and the Steinberg Torus.- Hints and Solutions.