Eulerian Numbers

• Main Author: Petersen, T. Kyle (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Birkhäuser, 2015.
• Series: Birkhäuser Advanced Texts Basler Lehrbücher,
• Subjects: Mathematics.; Group theory.; Number theory.; Topology.; Discrete mathematics.; Combinatorics.; Number Theory.; Group Theory and Generalizations.; Discrete Mathematics.

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, polytope...

Table of Contents:

• 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.