rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Eulerian Numbers
  name:
    name part: Petersen, T. Kyle.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2015
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVIII, 456 p. 78 illus., 4 illus. in color. online resource.
  abstract: 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.
  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.
  note: by T. Kyle Petersen.
  subject:
    topic: Mathematics
  subject:
    topic: Group theory
  subject:
    topic: Number theory
  subject:
    topic: Topology
  subject:
    topic: Discrete mathematics
  subject:
    topic: Combinatorics
  subject:
    topic: Mathematics
  subject:
    topic: Combinatorics
  subject:
    topic: Topology
  subject:
    topic: Number Theory
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Discrete Mathematics
  classification: QA164-167.2
  classification: 511.6
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Birkhäuser Advanced Texts Basler Lehrbücher
  identifier: 9781493930913
  identifier: http://dx.doi.org/10.1007/978-1-4939-3091-3
  record info:
    record creation date: 151012
    record change date: 20151030091401.0
    record identifier: 978-1-4939-3091-3