A Course in EnumerationSpringer Science & Business Media, 2007. gada 28. jūn. - 566 lappuses Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result. |
Saturs
| 2 | |
Formal Series and Infinite Matrices | 53 |
Generating Functions | 93 |
Hypergeometric Summation | 143 |
Sieve Methods | 179 |
Enumeration of Patterns | 239 |
The Catalan Connection | 289 |
Symmetric Functions | 345 |
Counting Polynomials | 393 |
Models from Statistical Physics | 451 |
Solutions to Selected Exercises | 519 |
Notation 553 | 552 |
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according Algebraic alternating appears apply bijection blocks called Catalan numbers clearly coefficients colors columns combinatorial compute connected Consider contains corresponding counting crossing cycle defined definition denote derive Determine diagram directed easily edges elements equal equation Eulerian Example Exercise expression faces figure Finally fixed formula function given gives graph graph G Hence holds identity implies induction inversion involution lattice Lemma length Let G look mappings matrix means Note obtain operator orientation pairs partitions path patterns permutations plane pn(x points polynomial precisely problem proof Proposition Prove recurrence result root sequence Show side similarly steps Suppose symmetric Theorem Theory tion trees unique usual vertex vertices walks weight Write yields