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Eulerian numbers

Petersen, T. Kyle.

Eulerian numbers

Record Type:	Electronic resources : Monograph/item
Title/Author:	Eulerian numbersby T. Kyle Petersen.
Author:	Petersen, T. Kyle.
Published:	New York, NY :Springer New York :2015.
Description:	xviii, 456 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Euler's numbers.
Online resource:	http://dx.doi.org/10.1007/978-1-4939-3091-3
ISBN:	9781493930913$q(electronic bk.)

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$q(electronic bk.)

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

731680
Euler's numbers.

LC Class. No.: QA246 / .P48 2015

Dewey Class. No.: 511.6

Eulerian numbers
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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 731680
650 0 $a Combinatorial enumeration problems. $3 190930
650 0 $a Combinatorial analysis. $3 182280
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Combinatorics. $3 274788
650 2 4 $a Topology. $3 185965
650 2 4 $a Number Theory. $3 274059
650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Discrete Mathematics. $3 524738
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Birkhauser advanced texts. $3 676329
856 4 0 $u http://dx.doi.org/10.1007/978-1-4939-3091-3
950 $a Mathematics and Statistics (Springer-11649)