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Algebraic combinatorics (Record no. 15656)

000 -Label
leader 02633 2200253 4500
010 ## - ISBN
ISBN 9781461469971
090 ## - Numéro biblio (koha)
Numéro biblioitem (koha) 15656
001 - Numéro de notice
Numéro d'identification notice 15656
101 ## - Langue
langue du document anglais
200 ## - Titre
titre propre Algebraic combinatorics
type de document Livre numérique
Auteur Richard P. Stanley
complément du titre walks, trees, tableaux, and more
210 ## - Editeur
lieu de publication New York
nom de l'éditeur Springer
date de publication cop. 2013
225 ## - collection
lien interne koha 181347
titre de la collection Undergraduate texts in mathematics
ISSN de la collection 2197-5604
titre de partie (Online)
300 ## - Note
note This book is intended to be a one-semester textbook for undergraduates. So its title seems a little bit too general. As the subtitle suggests, the eleven first chapters are brief introductions to some aspects of the theory of trees and graphs essentially using linear algebra. The twelth one is a potpourri of short problems of various kinds (counting, probability, algebraic number theory).

The first chapter counts the walks on a graph with the associated matrix. The second one specializes to the n-cube and the Radon transform. The third one is about random walks. From the fourth one on, posets are introduced, the Sperner property is studied, then Boolean algebras and the quotient poset by a subgroup of the symmetric group. Young diagrams and Polya’s theory of enumeration (coloring of combinatorial objects) follow in 6 and 7. Some formulas on Young tableaux are derived in Chapter 8, then in 9 the matrix-tree theorem counts the number of spanning trees of a graph. Eulerian tours lead to the notions of Eulerian digraph and oriented trees in Chapter 10. The overview of graph theory ends with some clues about electrical networks in Chapter 11. Each chapter is short enough and forms a “lesson” in some sense. They are often followed by notes and complements, and always end with a collection of exercices (some hints at the end of the book). Many figures illustrate the notions and the properties as they are introduced. (zbMath)
686 ## - Classification MSC
code du système msc
lien interne koha 161307
Indice 05C05
Libellé Combinatorics -- Graph theory
Sous-catégorie Trees
686 ## - Classification MSC
code du système msc
lien interne koha 161339
Indice 05C81
Libellé Combinatorics -- Graph theory
Sous-catégorie Random walks on graphs
686 ## - Classification MSC
code du système msc
lien interne koha 161324
Indice 05C50
Libellé Combinatorics -- Graph theory
Sous-catégorie Graphs and linear algebra (matrices, eigenvalues, etc.)
686 ## - Classification MSC
code du système msc
lien interne koha 161323
Indice 05C45
Libellé Combinatorics -- Graph theory
Sous-catégorie Eulerian and Hamiltonian graphs
686 ## - Classification MSC
code du système msc
lien interne koha 161317
Indice 05C30
Libellé Combinatorics -- Graph theory
Sous-catégorie Enumeration in graph theory
700 ## - Auteur
code de fonction Auteur
auteur Stanley
partie du nom autre que l'élément d'entrée Richard P.
koha internal code 177576
dates 1944-
856 ## - accès
URI http://link.springer.com/book/10.1007/978-1-4614-6998-8
note Springerlink
856 ## - accès
URI http://www.ams.org/mathscinet-getitem?mr=3097651
note MSN
856 ## - accès
URI https://zbmath.org/?q=an:1278.05002
note zbMath

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