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Eulerian numbers / T. Kyle Petersen.

By: Material type: TextTextSeries: Birkhauser advanced textsPublication details: New York : Birkhauser, 2015.Description: xviii, 456 p. : illustrations ; 25 cmISBN:
  • 9781493930906 (hbk)
Subject(s): DDC classification:
  • 511.6 23 P484
Contents:
1. Eulerian Numbers -- 2. Narayana Numbers -- 3. Partially Ordered Sets -- 4. Gamma-nonnegativity -- 5. Weak Order, Hyperplane Arrangements, and the Tamari Lattice -- 6. Refined Enumeration -- 7. Cubes, carries, and amazing matrix -- 8. Simplicial Complexes -- 9. Barycentric Subdivision -- 10. Characterizing f-vectors -- 11. Coxeter Groups -- 12. W-Narayana Numbers -- 13. Combinatorics for Coxeter groups of Types Bn and Dn -- 14. Affine Descents and the Steinberg Torus -- Hints and Solutions.
Summary: 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 511.6 P484 (Browse shelf(Opens below)) Checked out 13/02/2025 137087
Total holds: 0

Includes bibliographical references and index.

1. Eulerian Numbers --
2. Narayana Numbers --
3. Partially Ordered Sets --
4. Gamma-nonnegativity --
5. Weak Order, Hyperplane Arrangements, and the Tamari Lattice --
6. Refined Enumeration --
7. Cubes, carries, and amazing matrix --
8. Simplicial Complexes --
9. Barycentric Subdivision --
10. Characterizing f-vectors --
11. Coxeter Groups --
12. W-Narayana Numbers --
13. Combinatorics for Coxeter groups of Types Bn and Dn --
14. Affine Descents and the Steinberg Torus --
Hints and Solutions.

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.

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