Stanley R.P. Catalan numbers. - New York: Cambridge university press, 2015. - viii, 215 p.: ill. - Bibliogr.: p.201-204. - Ind.: p.205-215. - ISBN 978-1-107-42774-7 Шифр: (И/В17-S81) 02  Место хранения:   02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents

Preface ....................................................... vii 1 Basic Properties ............................................. 1 1.1 The Definition of Catalan Numbers ....................... 1 1.2 The Fundamental Recurrence .............................. 2 1.3 A Generating Function ................................... 3 1.4 An Explicit Formula ..................................... 4 1.5 Fundamental Combinatorial Interpretations ............... 5 1.6 A Combinatorial Proof .................................. 12 2 Bijective Exercises ......................................... 15 3 Bijective Solutions ......................................... 56 4 Additional Problems ........................................ 101 5 Solutions to Additional Problems ........................... 138 Appendix A In the beginning .................................. 171 Appendix В History of Catalan Numbers (by Igor Раk) .......... 177 B.l MingAntu .............................................. 177 B.2 Euler and Goldbach .................................... 178 B.3 Euler and Segner ...................................... 179 B.4 Kotelnikow and Fuss ................................... 180 B.5 The French School, 1838-1843 .......................... 181 B.6 The British School, 1857-1891 ......................... 182 B.7 The Ballot Problem .................................... 183 B.8 Later Years ........................................... 185 B.9 The Name .............................................. 186 B.10 The Importance ........................................ 187 Glossary ...................................................... 191 Bibliography .................................................. 201 Index ......................................................... 205