國立高雄大學圖資館 |

Language: English

Back

An introduction to catalan numbers

Roman, Steven.

An introduction to catalan numbers

Record Type:	Electronic resources : Monograph/item
Title/Author:	An introduction to catalan numbersby Steven Roman.
Author:	Roman, Steven.
Published:	Cham :Springer International Publishing :2015.
Description:	xii, 121 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Catalan numbers (Mathematics)
Online resource:	http://dx.doi.org/10.1007/978-3-319-22144-1
ISBN:	9783319221441$q(electronic bk.)

An introduction to catalan numbers
Roman, Steven.

An introduction to catalan numbers[electronic resource] /by Steven Roman. - Cham :Springer International Publishing :2015. - xii, 121 p. :ill., digital ;24 cm. - Compact textbooks in mathematics,2296-4568. - Compact textbooks in mathematics..

Introduction -- Dyck Words -- The Catalan Numbers -- Catalan Numbers and Paths -- Catalan Numbers and Trees -- Catalan Numbers and Geometric Widgits -- Catalan Numbers and Algebraic Widgits -- Catalan Numbers and Interval Structures -- Catalan Numbers and Partitions -- Catalan Numbers and Permutations -- Catalan Numbers and Semiorders -- Exercises -- Solutions and Hints -- Appendix A: A Brief Introduction to Partially Ordered Sets -- Appendix B: A Brief Introduction to Graphs and Trees -- Index.

This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. "Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers." - From the foreword by Richard Stanley.

ISBN: 9783319221441$q(electronic bk.)

Standard No.: 10.1007/978-3-319-22144-1doiSubjects--Topical Terms:

320814
Catalan numbers (Mathematics)

LC Class. No.: QA164

Dewey Class. No.: 511.6

An introduction to catalan numbers
LDR:02730nmm a2200325 a 4500 001 476947
003 DE-He213
005 20160414110910.0
006 m d
007 cr nn 008maaau
008 160526s2015 gw s 0 eng d
020 $a 9783319221441$q(electronic bk.)
020 $a 9783319221434$q(paper)
024 7 $a 10.1007/978-3-319-22144-1 $2 doi
035 $a 978-3-319-22144-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA164
072 7 $a PBV $2 bicssc
072 7 $a MAT036000 $2 bisacsh
082 0 4 $a 511.6 $2 23
090 $a QA164 $b .R758 2015
100 1 $a Roman, Steven. $3 185962
245 1 3 $a An introduction to catalan numbers $h [electronic resource] / $c by Steven Roman.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2015.
300 $a xii, 121 p. : $b ill., digital ; $c 24 cm.
490 1 $a Compact textbooks in mathematics, $x 2296-4568
505 0 $a Introduction -- Dyck Words -- The Catalan Numbers -- Catalan Numbers and Paths -- Catalan Numbers and Trees -- Catalan Numbers and Geometric Widgits -- Catalan Numbers and Algebraic Widgits -- Catalan Numbers and Interval Structures -- Catalan Numbers and Partitions -- Catalan Numbers and Permutations -- Catalan Numbers and Semiorders -- Exercises -- Solutions and Hints -- Appendix A: A Brief Introduction to Partially Ordered Sets -- Appendix B: A Brief Introduction to Graphs and Trees -- Index.
520 $a This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics. Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics. Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more. Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material. The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. "Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones. He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics. [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers." - From the foreword by Richard Stanley.
650 0 $a Catalan numbers (Mathematics) $3 320814
650 0 $a Mathematics. $3 184409
650 0 $a Computer science $x Mathematics. $3 181991
650 0 $a Sequences (Mathematics) $3 228268
650 0 $a Combinatorial analysis. $3 182280
650 0 $a Graph theory. $3 181880
650 2 4 $a Combinatorics. $3 274788
650 2 4 $a Graph Theory. $3 522732
650 2 4 $a Sequences, Series, Summability. $3 275704
650 2 4 $a Mathematical Applications in Computer Science. $3 530811
650 2 4 $a Discrete Mathematics in Computer Science. $3 274791
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Compact textbooks in mathematics. $3 700241
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-22144-1
950 $a Mathematics and Statistics (Springer-11649)