03447nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001600153072001600169072002300185082001400208100002800222245008200250250001800332264007900350300004400429336002600473337002600499338003600525347002400561490004900585505050500634520128401139650001702423650003502440650002902475650002602504650001902530650001802549650001702567650001902584650001802603650003602621650005102657650004602708710003402754773002002788776003602808830004902844856004802893978-3-319-22144-1DE-He21320180115171637.0cr nn 008mamaa151117s2015 gw | s |||| 0|eng d a97833192214417 a10.1007/978-3-319-22144-12doi 4aQA164-167.2 7aPBV2bicssc 7aMAT0360002bisacsh04a511.62231 aRoman, Steven.eauthor.13aAn Introduction to Catalan Numbersh[electronic resource] /cby Steven Roman. a1st ed. 2015. 1aCham :bSpringer International Publishing :bImprint: Birkhäuser,c2015. aXII, 121 p. 44 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aCompact Textbooks in Mathematics,x2296-45680 aIntroduction -- 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. aThis 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. 0aMathematics. 0aComputer sciencexMathematics. 0aSequences (Mathematics). 0aComputer mathematics. 0aCombinatorics. 0aGraph theory.14aMathematics.24aCombinatorics.24aGraph Theory.24aSequences, Series, Summability.24aMathematical Applications in Computer Science.24aDiscrete Mathematics in Computer Science.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783319221434 0aCompact Textbooks in Mathematics,x2296-456840uhttp://dx.doi.org/10.1007/978-3-319-22144-1