東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Eulerian numbers

Petersen, T. Kyle.

FindBook

Google Book

Amazon

博客來

Eulerian numbers

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Eulerian numbers/ by T. Kyle Petersen.
作者:	Petersen, T. Kyle.
出版者:	New York, NY :Springer New York : : 2015.,
面頁冊數:	xviii, 456 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Euler's numbers. -
電子資源:	http://dx.doi.org/10.1007/978-1-4939-3091-3
ISBN:	9781493930913

Eulerian numbers
Petersen, T. Kyle.

Eulerian numbers[electronic resource] /by T. Kyle Petersen. - New York, NY :Springer New York :2015. - xviii, 456 p. :ill., digital ;24 cm. - Birkhauser advanced texts,1019-6242. - Birkhauser advanced texts..

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.

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.

ISBN: 9781493930913

Standard No.: 10.1007/978-1-4939-3091-3doiSubjects--Topical Terms:

2162911
Euler's numbers.

LC Class. No.: QA246 / .P48 2015

Dewey Class. No.: 511.6

Eulerian numbers
LDR:02698nmm a2200325 a 4500 001 2013473
003 DE-He213
005 20160412115829.0
006 m d
007 cr nn 008maaau
008 160518s2015 nyu s 0 eng d
020 $a 9781493930913 $q (electronic bk.)
020 $a 9781493930906 $q (paper)
024 7 $a 10.1007/978-1-4939-3091-3 $2 doi
035 $a 978-1-4939-3091-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA246 $b .P48 2015
072 7 $a PBV $2 bicssc
072 7 $a MAT036000 $2 bisacsh
082 0 4 $a 511.6 $2 23
090 $a QA246 $b .P484 2015
100 1 $a Petersen, T. Kyle. $3 1920759
245 1 0 $a Eulerian numbers $h [electronic resource] / $c by T. Kyle Petersen.
260 $a New York, NY : $b Springer New York : $b Imprint: Birkhauser, $c 2015.
300 $a xviii, 456 p. : $b ill., digital ; $c 24 cm.
490 1 $a Birkhauser advanced texts, $x 1019-6242
505 0 $a 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.
520 $a 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.
650 0 $a Euler's numbers. $3 2162911
650 0 $a Combinatorial enumeration problems. $3 706042
650 0 $a Combinatorial analysis. $3 523878
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Combinatorics. $3 895617
650 2 4 $a Topology. $3 522026
650 2 4 $a Number Theory. $3 891078
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a Discrete Mathematics. $3 1569938
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Birkhauser advanced texts. $3 1050445
856 4 0 $u http://dx.doi.org/10.1007/978-1-4939-3091-3
950 $a Mathematics and Statistics (Springer-11649)