國立虎尾科技大學 |

Eulerian Numbers

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Eulerian Numbers/ by T. Kyle Petersen.
作者:	Petersen, T. Kyle.
面頁冊數:	XVIII, 456 p. 78 illus., 4 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Combinatorics. -
電子資源:	https://doi.org/10.1007/978-1-4939-3091-3
ISBN:	9781493930913

Eulerian Numbers
Petersen, T. Kyle.

Eulerian Numbers[electronic resource] /by T. Kyle Petersen. - 1st ed. 2015. - XVIII, 456 p. 78 illus., 4 illus. in color.online resource. - Birkhäuser Advanced Texts Basler Lehrbücher,1019-6242. - Birkhäuser Advanced Texts Basler Lehrbücher,.

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:

669353
Combinatorics.

LC Class. No.: QA164-167.2

Dewey Class. No.: 511.6

Eulerian Numbers
LDR:03126nam a22004095i 4500 001 963634
003 DE-He213
005 20200701160237.0
007 cr nn 008mamaa
008 201211s2015 xxu| s |||| 0|eng d
020 $a 9781493930913 $9 978-1-4939-3091-3
024 7 $a 10.1007/978-1-4939-3091-3 $2 doi
035 $a 978-1-4939-3091-3
050 4 $a QA164-167.2
072 7 $a PBV $2 bicssc
072 7 $a MAT036000 $2 bisacsh
072 7 $a PBV $2 thema
082 0 4 $a 511.6 $2 23
100 1 $a Petersen, T. Kyle. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1069782
245 1 0 $a Eulerian Numbers $h [electronic resource] / $c by T. Kyle Petersen.
250 $a 1st ed. 2015.
264 1 $a New York, NY : $b Springer New York : $b Imprint: Birkhäuser, $c 2015.
300 $a XVIII, 456 p. 78 illus., 4 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Birkhäuser Advanced Texts Basler Lehrbücher, $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 Combinatorics. $3 669353
650 0 $a Topology. $3 633483
650 0 $a Number theory. $3 527883
650 0 $a Group theory. $3 527791
650 0 $a Discrete mathematics. $3 1254302
650 2 4 $a Number Theory. $3 672023
650 2 4 $a Group Theory and Generalizations. $3 672112
650 2 4 $a Discrete Mathematics. $3 796600
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9781493930906
776 0 8 $i Printed edition: $z 9781493930920
776 0 8 $i Printed edition: $z 9781493947942
830 0 $a Birkhäuser Advanced Texts Basler Lehrbücher, $x 1019-6242 $3 1258676
856 4 0 $u https://doi.org/10.1007/978-1-4939-3091-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)