Eulerian Numbers (Birkhäuser Advanced Texts Basler Lehrbücher)

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9781493930906: Eulerian Numbers (Birkhäuser Advanced Texts Basler Lehrbücher)

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

About the Author :

T. Kyle Petersen is an Associate Professor of Mathematics at DePaul University, Chicago, USA.  His research areas include algebraic, enumerative, and topological combinatorics.  He received his PhD in Mathematics from Brandeis University.

Review :

“This work offers wonderful material to supplement a course in combinatorics or discrete mathematics, or for a stimulating capstone course. Summing Up: Highly recommended. Lower-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 53 (11), July, 2016)

“This book serves dual purposes. On the one hand, it is a monograph on Eulerian numbers and their generalizations. ... On the other hand, the book gives an introduction to contemporary enumerative, algebraic and geometric combinatorics, and it can be used as a text at beginning graduate or advanced undergraduate level. ... This is a well-written text for a good course.” (László A. Székely, zbMATH 1337.05001, 2016)

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

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Description du livre Birkhauser, Switzerland, 2015. Hardback. État : New. 1st ed. 2015. Language: English . Brand New Book. 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.â. N° de réf. du libraire AAU9781493930906

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T. Kyle Petersen
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Description du livre Birkhauser, Switzerland, 2015. Hardback. État : New. 1st ed. 2015. Language: English . Brand New Book. 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.â. N° de réf. du libraire AAU9781493930906

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Description du livre Birkh?user, 2015. État : New. Series: Birkhauser Advanced Texts / Basler Lehrbucher. Num Pages: 456 pages, 74 black & white illustrations, 4 colour illustrations, 41 black & white tables, biograph. BIC Classification: PBD; PBH; PBP; PBV. Category: (P) Professional & Vocational. Dimension: 166 x 245 x 30. Weight in Grams: 1006. . 2015. 1st ed. 2015. Hardcover. . . . . . N° de réf. du libraire V9781493930906

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Description du livre Birkhäuser. État : New. Series: Birkhauser Advanced Texts / Basler Lehrbucher. Num Pages: 456 pages, 74 black & white illustrations, 4 colour illustrations, 41 black & white tables, biograph. BIC Classification: PBD; PBH; PBP; PBV. Category: (P) Professional & Vocational. Dimension: 166 x 245 x 30. Weight in Grams: 1006. . 2015. 1st ed. 2015. Hardcover. . . . . Books ship from the US and Ireland. N° de réf. du libraire V9781493930906

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