The Resource Eulerian Numbers, by T. Kyle Petersen, (electronic resource)
Eulerian Numbers, by T. Kyle Petersen, (electronic resource)
Resource Information
The item Eulerian Numbers, by T. Kyle Petersen, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Eulerian Numbers, by T. Kyle Petersen, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- XVIII, 456 p. 78 illus., 4 illus. in color.
- 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
- Isbn
- 9781493930913
- Label
- Eulerian Numbers
- Title
- Eulerian Numbers
- Statement of responsibility
- by T. Kyle Petersen
- Language
- eng
- 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
- http://library.link/vocab/creatorName
- Petersen, T. Kyle
- Image bit depth
- 0
- Literary form
- non fiction
- http://library.link/vocab/relatedWorkOrContributorName
- SpringerLink (Online service)
- Series statement
- Birkhäuser Advanced Texts Basler Lehrbücher,
- http://library.link/vocab/subjectName
-
- Mathematics
- Group theory
- Number theory
- Topology
- Discrete mathematics
- Combinatorics
- Label
- Eulerian Numbers, by T. Kyle Petersen, (electronic resource)
- Antecedent source
- mixed
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier.
- Color
- not applicable
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent.
- 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
- Control code
- 978-1-4939-3091-3
- Dimensions
- unknown
- Extent
- XVIII, 456 p. 78 illus., 4 illus. in color.
- File format
- multiple file formats
- Form of item
- electronic
- Governing access note
- Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
- Isbn
- 9781493930913
- Level of compression
- uncompressed
- Media category
- computer
- Media MARC source
- rdamedia.
- Media type code
-
- c
- Other control number
- 10.1007/978-1-4939-3091-3
- Other physical details
- online resource.
- Quality assurance targets
- absent
- Reformatting quality
- access
- Specific material designation
- remote
- System control number
- (OCoLC)985047924
- Label
- Eulerian Numbers, by T. Kyle Petersen, (electronic resource)
- Antecedent source
- mixed
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier.
- Color
- not applicable
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent.
- 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
- Control code
- 978-1-4939-3091-3
- Dimensions
- unknown
- Extent
- XVIII, 456 p. 78 illus., 4 illus. in color.
- File format
- multiple file formats
- Form of item
- electronic
- Governing access note
- Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
- Isbn
- 9781493930913
- Level of compression
- uncompressed
- Media category
- computer
- Media MARC source
- rdamedia.
- Media type code
-
- c
- Other control number
- 10.1007/978-1-4939-3091-3
- Other physical details
- online resource.
- Quality assurance targets
- absent
- Reformatting quality
- access
- Specific material designation
- remote
- System control number
- (OCoLC)985047924
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.eui.eu/portal/Eulerian-Numbers-by-T.-Kyle-Petersen/KZq8Rl3A4iY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/Eulerian-Numbers-by-T.-Kyle-Petersen/KZq8Rl3A4iY/">Eulerian Numbers, by T. Kyle Petersen, (electronic resource)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.eui.eu/portal/Eulerian-Numbers-by-T.-Kyle-Petersen/KZq8Rl3A4iY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/Eulerian-Numbers-by-T.-Kyle-Petersen/KZq8Rl3A4iY/">Eulerian Numbers, by T. Kyle Petersen, (electronic resource)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>
