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010   $a3-319-22144-2
024 7 $a10.1007/978-3-319-22144-1
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035   $a(SSID)ssj0001585224
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035   $a(PQKBTitleCode)TC0001585224
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035   $a(DE-He213)978-3-319-22144-1
035   $a(MiAaPQ)EBC6315618
035   $a(MiAaPQ)EBC5586770
035   $a(Au-PeEL)EBL5586770
035   $a(OCoLC)1066196728
035   $a(PPN)190525452
035   $a(EXLCZ)993710000000521692
100   $a20151117d2015      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 13$aAn Introduction to Catalan Numbers /$fby Steven Roman
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2015.
215   $a1 online resource (XII, 121 p. 44 illus.) 
225 1 $aCompact Textbooks in Mathematics,$x2296-455X
300   $aIncludes index.
311 08$a3-319-22143-4 
327   $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.
330   $aThis textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics.  Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics.  Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more.  Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material.  The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. ?Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones.  He has made an excellent choice of topics in order to convey the flavor of Catalan combinatorics.  [Readers] will acquire a good feeling for why so many mathematicians are enthralled by the remarkable ubiquity and elegance of Catalan numbers.?  - From the foreword by Richard Stanley.
410  0$aCompact Textbooks in Mathematics,$x2296-455X
606   $aDiscrete mathematics
606   $aGraph theory
606   $aSequences (Mathematics)
606   $aComputer science$xMathematics
606   $aDiscrete Mathematics
606   $aGraph Theory
606   $aSequences, Series, Summability
606   $aMathematical Applications in Computer Science
606   $aDiscrete Mathematics in Computer Science
615  0$aDiscrete mathematics.
615  0$aGraph theory.
615  0$aSequences (Mathematics).
615  0$aComputer science$xMathematics.
615 14$aDiscrete Mathematics.
615 24$aGraph Theory.
615 24$aSequences, Series, Summability.
615 24$aMathematical Applications in Computer Science.
615 24$aDiscrete Mathematics in Computer Science.
676   $a511.6
700   $aRoman$b Steven$4aut$4http://id.loc.gov/vocabulary/relators/aut$057255
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300257203321
996   $aIntroduction to Catalan numbers$91522750
997   $aUNINA